746 Video Lessons

Select the section below that fits the topic that you need help on. All our 746 Algebra 2 videos are linked to our YouTube Channel and are Free to watch. Enjoy!

## BASICS – 29 Video Lessons

## REVIEW OF ALGEBRAIC AND NUMERIC EXPRESSIONS

- (7 – 2) ÷ 5
- (3 + 3)^2
- (6 – 3)^2
- 5 + (16 + 2) ÷ 3
- (-6 x 2) ÷ -3
- 2 + 12 ÷ 2 + 1
- -4 – (1 – 5) – (-4)^2
- -3 x 2 x 2(-3 – 1)
- (4 – 3)(1 – (3 + 5)) x 5
- ((-16 – (-2 + 1)) x 2) ÷ 5
- 2 – 8 ÷ -2 – 3 – -12 ÷ -6 x -2
- (-11 – 6 – -5 + 1 + 3 x 2) ÷ -5
- y + z + 2; use y = -6 and z = 5
- p(q ÷ 3 – p); use p = -6 and q = -3
- z ÷ 6 + x + x – 5; use x = 1 and z=6
- x(z + 3) + 1 + 3 – y; use x= 6, y = -5 and z = 2
- 6 + q + 5 – (p – q) + 15; use p = 1 and q = 1
- -3 ÷ 3(a + c(b+5) – (-6 + a)); use a = 1, b = -6 and c = -4
- 9x + 9 – 1
- 10n – 4n
- -9 – 6(-v + 5)
- -10(-8x + 9) – 8x
- 1 + 4(2 – 3k)
- -8v + 6(10 + 6v)
- 7(1 + 9v) – 8(-5v – 6)
- -10(x – 7) – 7(x + 2)
- -2(-6x – 9) – 4(x + 9)
- 9(7k + 8) + 3(k – 10)

## EQUATIONS AND INEQUALITIES – 84 Video Lessons

## SOLVING MULTI-STEP EQUATIONS

- 4n – 2n = 4
- -12 = 2 + 5v + 2v
- 3 = x + 3 – 5x
- x + 3 – 3 = -6
- -12 = 3 – 2k – 3k
- -1 = -3r + 2r
- 6 = -3(x + 2)
- -3(4r – 8) = -36
- 24 = 6(-x – 3)
- 75 = 3(-6n – 5)
- -3(1 + 6r) = 14 – r
- 6(6v + 6) – 5 = 1 + 6v
- -4k + 2(5k – 6) = -3k – 39
- -16 + 5n = -7(-6 + 8n) + 3
- 10p + 9 – 11 – p = -2(2p + 4) – 3(2p – 2)
- -10n + 3(8 + 8n) = -6(n – 4)
- 10(x + 3) – (-9x – 4) = x – 5 + 3
- 12(2k + 11) = 12(2k + 12)
- -12(x – 12) = -9(1 + 7x)
- -11 + 10(p+10) = 4 – 5(2p + 11)
- Solve two ways: 20 = 5(-3 + x)

## WORK WORD PROBLEMS

- It takes Kali eight minutes to sweep a porch. Shawna can sweep the same porch in 11 minutes. If they worked together how long would it take them?
- It takes Heather seven hours to pour a large concrete driveway. Alberto can pour the same driveway in eight hours. How long would it take them if they worked together?
- Working alone, it takes Stephanie seven hours to clean an attic. Shayna can clean the same attic in 12 hours. Find how long it would take them if they worked together.
- It takes Darryl nine hours to mop a warehouse. Castel can mop the same warehouse in eight hours. Find how long it would take them if they worked together.
- Working alone, Shanice can tar a roof in 12 hours. One day her friend Kathryn helped her and it only took 5.14 hours. How long would it take Kathryn to do it alone?
- Nicole can pick forty bushels of apples in 15 hours. Carlos can pick the same amount in 11 hours. How long would it take them if they worked together?
- Working together, Arjun and Maria can oil the lanes in a bowling alley in 4.24 hours. Had she done it alone it would have taken Maria eight hours. How long would it take Arjun to do it alone?
- Working alone, Eduardo can harvest a field in 14 hours. One day his friend Amy helped him and it only took 7.47 hours. How long would it take Amy to do it alone?
- Working together, Mary and Trevon can inflate twenty balloons in 7.34 minutes. Had he done it alone it would have taken Trevon 14.1 minutes. How long would it take Mary to do it alone?
- Shreya can weed a garden in 19.3 minutes. One day her friend Elisa helped her and it only took 7.44 minutes. Find how long it would take Elisa to do it alone.
- Huong can wash a car in 10 minutes. One day her friend Castel helped her and it only took 6.67 minutes. How long would it take Castel to do it alone?
- Working together, Kim and Jennifer can install a new deck in 6.28 hours. Had she done it alone it would have taken Jennifer 13.7 hours. How long would it take Kim to do it alone?

## DISTANCE-RATE-TIME WORD PROBLEMS

- A container ship left the Dania Pier and traveled north. An aircraft carrier left four hours later traveling at 30 mph in an effort to catch up to the container ship. After traveling for eight hours the aircraft carrier finally caught up. What was the container ship’s average speed?
- A cruise ship made a trip to Guam and back. The trip there took 12 hours and the trip back took nine hours. It averaged 20 km/h on the return trip. Find the average speed of the trip there.
- Scott left the airport and traveled toward the train station. Three hours later Castel left traveling at 50 mph in an effort to catch up to Scott. After traveling for two hours Castel finally caught up. What was Scott’s average speed?
- Jose traveled to the town hall and back. The trip there took five hours and the trip back took four hours. He averaged 35 km/h on the return trip. Find the average speed of the trip there.
- Perry left school driving toward the lake one hour before Jaidee. Jaidee drove in the opposite direction going 6 mph slower than Perry for one hour after which time they were 174 mi. apart. What was Perry’s speed?
- Wilbur left the hardware store and traveled toward the recycling plant at an average speed of 33 km/h. Mary left two hours later and traveled in the same direction but with an average speed of 55 km/h. How long did Wilbur travel before Mary caught up?
- An aircraft carrier left Hawaii traveling west seven hours before a container ship. The container ship traveled in the opposite direction going 5 km/h slower than the aircraft carrier for six hours after which time the ships were 540 km apart. Find the aircraft carrier’s speed.
- A submarine left the Azores and traveled west. Three hours later an aircraft carrier left traveling 3 mph faster in an effort to catch up to it. After seven hours the aircraft carrier finally caught up. Find the submarine’s average speed.
- Jimmy drove to his cabin on the lake and back. It took 0.6 hours longer to go there than it did to come back. The average speed on the trip there was 46 km/h. The average speed on the way back was 52 km/h. How many hours did the trip there take?
- Anjali traveled to the recycling plant and back. The trip there took 5.8 hours and the trip back took 5.1 hours. She averaged 7 mph faster on the return trip than on the outbound trip. What was Anjali’s average speed on the outbound trip?
- A fishing boat left Hawaii traveling west 0.5 hours before a cruise ship. The cruise ship traveled in the opposite direction going 12.5 km/h faster than the fishing boat for 11 hours after which time the ships were 322 km apart. What was the fishing boat’s speed?
- A diesel train left the station traveling north 1.5 hours before a freight train. The freight train traveled in the opposite direction going 6 km/h faster than the diesel train for two hours after which time the trains were 312.3 km apart. Find the diesel train’s speed.

## MIXTURE WORD PROBLEMS

- 7 kg of soybean oil which costs $4/kg were combined with 14 kg of canola oil which costs $1/kg. Find the cost per kg of the mixture.
- A sugar solution was made by mixing 8 qt. of a 2% sugar solution and 6 qt. of a 51% sugar solution. Find the concentration of the new mixture.
- A sugar solution was made by mixing 7 ml of a 50% sugar solution and 3 ml of a 80% sugar solution. Find the concentration of the new mixture.
- For her birthday party Kathryn mixed together 3 gal. of Brand A fruit punch and 6 gal. of Brand B. Brand A contains 17% fruit juice and Brand B contains 26% fruit juice. What percent of the mixture is fruit juice?
- How many gal. of a 65% saline solution must be mixed with 8 gal. of pure water to make a 25% solution?
- 1 oz of walnuts were mixed with 4 oz of peanuts which cost $4/oz to make mixed nuts which cost $5/oz. What is the price per oz of walnuts?
- Heather wants to make a 36% acid solution. She has already poured 3 fl. oz. of a 72% acid solution into a beaker. How many fl. oz. of a 9% acid solution must she add to this to create the desired mixture?
- Kali mixed together 9 gal. of Brand A fruit drink and 6 gal. of Brand B fruit drink which contains 5% fruit juice. Find the percent of fruit juice in Brand A if the mixture contained 11% fruit juice.
- To build the garden of your dreams you need 10 ft3 of soil containing 17% clay.

You have two types of soil you can combine to achieve this: soil with 35% clay and soil with 10% clay. How much of each soil should you use? - Bronze which costs $9.10/kg is made by combining copper which costs $8.90/kg with tin which costs $9.50/kg. Find the number of kg of copper and tin required to make 15.3 kg of bronze.
- Kristin wants to make 6 gal. of a 34% alcohol solution by mixing together a 24% alcohol solution and a 64% alcohol solution. How much of each solution must she use?
- Bronze which costs $7.05/kg is made by combining copper which costs $6.20/kg with tin which costs $8.70/kg. Find the number of kg of copper and tin required to make 5 kg of bronze.

## SOLVING INEQUALITIES

- 0 > 3x – 3 – 6
- 4x + 1 – 1 ≥ -8
- -1 ≤ 2n + 4 – 5
- -6 > 5n + 5 + 4
- 0 ≤ 2n + 3n
- 2p – 4p ≤ -2
- 7 < -(-k – 3) + 2
- 3 – 2(n – 4) > -1
- -5(1 – 4a) > -5
- -2(b + 1) + 4 < 10
- a – 15 > -4(-6 + 3a)
- 3(6b – 1) > 18 – 3b
- 26 + m ≥ 5(-6 + 3m)
- 20 – 2p > -2(p + 2) + 4p
- x + 1 + 1 + 6x > 3(x – 4) – (x – 4)
- -6(1 + 6x) < 6(1 – 5x)
- 2(1 – 4r) < -2(r + 3) – 4
- -6(1 + 2x) ≥ 6(2x – 1) + 2x
- -2(1 – 5x) > -(x + 1) – 1
- 5x – (x + 2) > -5(1 + x) + 3
- Write an inequality with x on both sides whose solution is x ≥ 2
- Name one particular solution to question # 20

## SYSTEMS OF EQUATIONS AND INEQUALITIES – 74 Video Lessons

## SYSTEMS OF TWO EQUATIONS

- y = -3x + 4 and y = 3x – 2
- y = x + 2 and x = -3
- x – y = 3 and 7x – y = -3
- 4x + y = 2 and x – y = 3
- y = 4x – 9 and y = x – 3
- 4x + 2y = 10 and x – y = 13
- y = -5 and 5x + 4y = -20
- x + 7y = 0 and 2x – 8y = 22
- 6x + 8y = -22 and y = -5
- -7x + 2y = 18 and 6x + 6y = 0
- 7x + 2y = -19 and -x + 2y = 21
- 3x – 5y = 17 and y = -7
- -7x + 4y = 24 and 4x – 4y = 0
- 4x – y = 2- and -2x – 2y = 10
- 8x – 6y = -20 and -16x + 7y = 30
- 6x – 12y = 24 and – x – 6y = 4
- -8x – 10y = 24 and 6x + 5y = 2
- -24 – 8x = 12y and 1 + (5/9)y = -(7/18)x
- -4y – 11x = 36 and 20 = -10x – 10y
- -9 + 5y = -4x and -11x = -20 + 9y
- 0 = -2y + 10 – 6x and 14 – 22y = 18x
- -16y = 22 + 6x and -11y – 4x = 15
- -16 + 20x – 8y = 0 and 36 = -18y – 22x
- -(5/7) – (11/7)x = -y and 2y = 7 + 5x
- Write a system of equations with the solution (4,-3)

## SYSTEMS OF TWO EQUATIONS WORD PROBLEMS

- The school that Lisa goes to is selling tickets to the annual talent show. On the first day of ticket sales the school sold 4 senior citizen tickets and 5 student tickets for a total of $102. The school took in $126 on the second day by selling 7 senior citizen tickets and 5 student tickets. What is the price each of one senior citizen ticket and one student ticket?
- Flying with the wind a plane went 183 km/h. Flying into the same wind the plane only went 141 km/h. Find the speed of the plane in still air and the speed of the wind.
- Castel and Gabriella are selling pies for a school fundraiser. Customers can buy apple pies and lemon meringue pies. Castel sold 6 apple pies and 4 lemon meringue pies for a total of $80. Gabriella sold 6 apple pies and 5 lemon meringue pies for a total of $94. What is the cost each of one apple pie and one lemon meringue pie?
- The school that Imani goes to is selling tickets to the annual dance competition. On the first day of ticket sales the school sold 3 senior citizen tickets and 3 child tickets for a total of $69. The school took in $91 on the second day by selling 5 senior citizen tickets and 3 child tickets. What is the price each of one senior citizen ticket and one child ticket?
- Ming and Carlos are selling cookie dough for a school fundraiser. Customers can buy packages of chocolate chip cookie dough and packages of gingerbread cookie dough. Ming sold 8 packages of chocolate chip cookie dough and 12 packages of gingerbread cookie dough for a total of $364. Carlos sold 1 package of chocolate chip cookie dough and 4 packages of gingerbread cookie dough for a total of $93. Find the cost each of one package of chocolate chip cookie dough and one package of gingerbread cookie dough.
- Kayla’s school is selling tickets to the annual dance competition. On the first day of ticket sales the school sold 3 senior citizen tickets and 5 child tickets for a total of $70. The school took in $216 on the second day by selling 12 senior citizen tickets and 12 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.
- A plane traveled 580 miles to Ankara and back. The trip there was with the wind. It took 5 hours. The trip back was into the wind. The trip back took 10 hours. Find the speed of the plane in still air and the speed of the wind.
- Amanda and Ndiba are selling flower bulbs for a school fundraiser. Customers can buy packages of tulip bulbs and bags of daffodil bulbs. Amanda sold 6 packages of tulip bulbs and 12 bags of daffodil bulbs for a total of $198. Ndiba sold 7 packages of tulip bulbs and 6 bags of daffodil bulbs for a total of $127. Find the cost each of one package of tulips bulbs and one bag of daffodil bulbs.
- The local amusement park is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 16 vans and 8 buses with 752 students. High School B rented and filled 5 vans and 5 buses with 380 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?
- The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 16 vans and 5 buses with 417 students. High School B rented and filled 10 vans and 8 buses with 480 students. Every van had the same number of students in it as did the buses. How many students can a van carry? How many students can a bus carry?
- The senior classes at High School A and High School B planned separate trips to the water park. The senior class at High School A rented and filled 14 vans and 16 buses with 1086 students. High School B rented and filled 10 vans and 13 buses with 870 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.
- Yellowstone National Park is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 7 vans and 10 buses with 332 students. High School B rented and filled 4 vans and 15 buses with 459 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus.

## SOLVING SYSTEMS OF THREE EQUATIONS WITH ELIMINATION

- −x − 5y − 5z = 2, 4x − 5y + 4z = 19, x + 5y − z = −20
- −4x − 5y − z = 18, −2x − 5y − 2z = 12, −2x + 5y + 2z = 4
- −x − 5y + z = 17, −5x − 5y + 5z = 5, 2x + 5y − 3z = −10
- 4x + 4y + z = 24, 2x − 4y + z = 0, 5x − 4y − 5z = 12
- 4r − 4s + 4t = −4, 4r + s − 2t = 5, −3r − 3s − 4t = −16
- x − 6y + 4z = −12, x + y − 4z = 12, 2x + 2y + 5z = −15
- x − y − 2z = −6, 3x + 2y = −25, −4x + y − z = 12
- 5a + 5b + 5c = −20, 4a + 3b + 3c = −6, −4a + 3b + 3c = 9
- −6r + 5s + 2t = −11, −2r + s + 4t = −9, 4r − 5s + 5t = −4
- −6x − 2y + 2z = −8, 3x − 2y − 4z = 8, 6x − 2y − 6z = −18
- 5x − 4y + 2z = 21, −x − 5y + 6z = −24, −x − 4y + 5z = −21
- 6r − s + 3t = −9, 5r + 5s − 5t = 20, 3r − s + 4t = −5
- −3a − b − 3c = −8, −5a + 3b + 6c = −4, −6a − 4b + c = −20
- −5x + 3y + 6z = 4, −3x + y + 5z = −5, −4x + 2y + z = 13
- 3a − 3b + 4c = −23, a + 2b − 3c = 25, 4a − b + c = 25
- −6x − 2y − z = −17, 5x + y − 6z = 19, −4x − 6y − 6z = −20
- Write a system of equations with the solution (2, 1, 0).

## SOLVING SYSTEMS OF THREE EQUATIONS WITH SUBSTITUTION

- −x− y−3z=−9, z = −3x − 1, x = 5y − z + 23
- x=−4z−19, y = 5x + z − 4, −5y − z = 25
- y=x+z+5, z = −3y − 3, 2x− y=−4
- −2y+5z=−3, y = −5x − 4z − 5, x=4z+4
- y=x+4z−5, 4x + 3y − 2z = 5, z = −2x + 2
- x=3y−3z+8, z = 4x + 5y − 14, 3y + 2z = 14
- −5x−3y+z=−4, −2x − 2y + 2z = 4, z = x + 5
- −4x+2z=14, y = x + z + 12, −2x − 4z = 22
- 3x−3y=−6, z = −3x − 3y + 9, −4x + 5y + z = 8
- x=−5y+4z+1, x − 2y + 3z = 1, 2x + 3y − z = 2
- a−2b+c=−6, a + 5c = −12, −a + 6b + 4c = 3
- −2x+3y+5z=−21, −4z = 20, 6x − 3y = 0
- 2x−4z=20, −3x+ y−4z=20, −4x + 2y + 3z = −15
- x+3y=−17, 3x=−6, 4x − 3y + 6z = 25
- 5r+4s−6t=−24, −2s + 2t = 0, s − t = 2
- −5r+5s+3t=−23, −5r + 3s − 3t = −11, −6r + 6t = −12

## COMPLEX NUMBERS – 60 Video Lessons

## OPERATIONS WITH COMPLEX NUMBERS

- i + 6i
- 3 + 4 + 6i
- 3i + i
- -8i – 7i
- 1 – 8i – 4 – i
- 7 + I + 4 + 4
- -3 + 6i – (-5 – 3i) – 8i
- 3 + 3i + 8 – 2i – 7
- 4i(-2 – 8i)
- 5i • -i
- 5i • i • -2i
- -4i • 5i
- (-2 – i)(4 + i)
- (7 – 6i)(-8 + 3i)
- 7i•3i(-8 – 6i)
- (4 – 5i)(4 + i)
- (2 – 4i)(-6 + 4i)
- (-3 + 2i)(-6 – 8i)
- (8 – 6i)(-4 – 4i)
- (1 – 7i)^2
- 6(-7 + 6i)(-4 + 2i)
- (-2 – 2i)(-4 – 3i)(7 + 8i)
- 5i + 7i • i
- (6i)^3
- 6i • -4i + 8
- -6(4 – 6i)
- (8 – 3i)^2
- 3 + 7i – 3i – 4
- -3i • 6i – 3(-7 + 6i)
- -6i(8 – 6i)(-8 – 8i)
- Simplify (2 + x)(3 – 2x) and (2 + i)(3 – 2i). How are they different?
- Simplify 2 + x – (3 – 2x) and 2 + i – (3 – 2i). How are they different?

## RATIONALIZING IMAGINARY DENOMINATORS

## QUADRATIC FUNCTIONS AND INEQUALITIES – 145 Video Lessons

## FACTORING QUADRATIC EXPRESSIONS

- x^2-7x-18
- p^2-5p-14
- m^2-9m+8
- x^2-16x+63
- 7x^2-31x-20
- 7k^2+9k
- 7x^2-45x-28
- 2b^2+17b+21
- 5p^2-p-18
- 28n^4+16n^3-80n^2
- 3b^2-5b^2+2b
- 7x^2-32x-60
- 30n^2b-87nb+30b
- 9r^2-5r-10
- 9p^2+73pr+70r
- 9x^2+7x-56
- 4x^3+43x^2+30
- 10m^2+89m-9
- For what values of b is the expression factorable? x^2+bx+12
- Name four values of b which make the expression factorable: x^2-3x+b

## SOLVING QUADRATIC EQUATIONS BY FACTORING

- (3n−2)(4n+1) = 0
- m(m−3) = 0
- (5n−1)(n+1) = 0
- (n+2)(2n+5) = 0
- 3k^2+72 = 33k
- n^2 = −18−9n
- 7v^2−42 = −35v
- k^2 = −4k−4
- −2v^2−v+12 = −3v^2+6v
- −4n^2+6n−16 = −5n^2
- 8r^2+3r+2 = 7r^2
- b^2+b = 2
- 10n^2−35 = 65n
- 3x^2−8x = 16
- 16n^2−114n = −14
- 28n^2 = −96−184n
- 7a^2+32 = 7−40a
- 42x^2−69x+20 = 7x^2−8
- True or False:If a quadratic equation can be factored and each factor contains only real numbers then there cannot be an imaginary solution.
- True or False: If a quadratic equation cannot be factored then it will have at least one imaginary solution.

## SOLVING QUADRATIC EQUATIONS BY COMPLETING THE SQUARE

## UNDERSTANDING THE DISCRIMINANT

- 6p^2-2p-3=0
- -2x^2-x-1=0
- -4m^2-4m+5=0
- 5b^2+b-2=0
- r^2+5r+2=0
- 2p^2+5p-4=0
- 9n^2-3n-8=-10
- -2x^2-8x-14=-6
- 9m^2+6m+6=5
- 4a^2=8a-4
- -9b^2=-8b+8
- -x^2-9=6x
- -4r^2-4r=6
- 8b^2-6b+3=5b^2
- -6x^2-6=-7x-9
- 4k^2+5k+4=-3k
- -7n^2+16n=8n
- 2x^2=10x+5
- -10n^2-3n-9=-2n
- -9r^2-8r-1=r-r^2-9
- -3p^2+10p+5=-8p^2
- m^2+5m=2m^2
- Write a quadratic equation that has two imaginary solutions.
- In your own words explain why a quadratic equation can’t have one imaginary solution.

## POLYNOMIAL FUNCTIONS – 118 Video Lessons

## BASIC POLYNOMIAL OPERATIONS

- -10x
- -10r^4 – 8r^2
- 7
- 9a^6 + 3a^5 – 4a^4 – 3a^2 + 9
- -3n^3 + n^2 – 10n + 9
- 7x^2 – 9x – 10
- -4b
- -9 + 7n^3 – n^2
- Why is it impossible to have a linear trinomial with one variable?
- (4m^4 – m^2) + (5m^2 + m^4)
- (5x + x^4) – (3x^4 + 4x)
- (5 + 7x^3 + 3x^2) + (-12 + 5x + 6x^2)
- (4 + 3x^2 + 8x^3) + (-7x^3 + 12x^5 + 6x^2)
- (13m^4 + 2) + (m^4n^2 + 2 – 2n^4) – (-13m^2n^3 + 5m^4)
- (-10mn^3 – 4n^4) – (-2n^4 – 7mn^3 – 6n^3) – (5n^3 + 6mn^3)
- (2n + 3)(n – 2)
- (5v – 1)(4v + 3)
- (2r – 2)(-r – 7)
- (3x + 5)(3x – 6)
- (-4x^2 – 5x – 1)(4x^2 – 6x – 2)
- (x^2 – 2x – 8)(-x^2 + 3x – 5)
- (-4m – 4n)(-6m – 6n)
- (8u + 4v)(6u + 6v)
- Simplify: (a + b)(c + d)
- Simplify then classify: 2x + 3x^2(4x – 5)

## FACTORING BY GROUPING

- 12a^3-9a^2+4a-3
- 2p^3+5p^2+6p+15
- 3n^3-4n^2+9n-12
- 12n^3+4n^2+3n+1
- m^3-m^2+2m-2
- 5n^3-10n^2+3n-6
- 35xy-5x-56y+8
- 224az+56ac-84yz-21yc
- mz-5mh^2-5nz+25nh^2
- 12xy-28x-15y+35
- 40xy+30x-100y-75
- 75a^2c-45a^2d-30bc+18bd
- 192x^2y+72x^3-24rxy-9rx^2
- 90au-36av-150yu+60yv
- 140ab-60a^2+168b-72a
- 105ab-90a-21b+18
- 16x^2c+8xyd-16x^2d-8xyc
- 150m^2nz+20mn^2c-120m^2nc-25mn^2z
- 105xuv+60xv-70xu-90xv^2
- 112xy-16x+128x^2-14y

## FACTORING QUADRATIC FORM

- u^4+2u^2
- x^4+x^2-12
- a^4+6a^2+5
- x^4-8x^2+15
- u^4-4u^2-5
- m^4+9m^2+20
- x^4+4x^2+3
- x^4-7x^2+10
- 7m^4-54m^2-16
- 7u^4+41u^2+30
- 5x^4-9x^2+4
- 3x^5-2x^3-8x
- 2x^6+13x^4+6x^2
- 2a^4-6a^2+9
- 7m^4-44m^2+12
- 3u^4-u^2-14
- x^6-9x^3+8
- 6x^9n-30x^5n-300xn
- x^6+4x^3-60
- 5nu^8-15nu^4+40n
- x^6+2x^3-3
- m^6-81
- -x^6+2x^3+15
- x^7m+2x^4m-15xm
- Why is this not in quadratic form? x^6+5x^4+6
- Factor: x^2n+9x^n-10

## GENERAL FUNCTIONS – 42 Video Lessons

## EVALUATING FUNCTIONS

- h(t) = |t + 2| + 3; find h(6)
- g(a) = 3^(3a – 2)
- w(t) = -2t + 1; find w(-7)
- g(x) = 3x – 3; find g(-6)
- h(n) = -2n^2 + 4
- h(t) = -2 • 5^(-t – 1); find h(-2)
- f(x) = x^2 – 3x; find f(-8)
- p(a) = -4^3a; find p(-1)
- p(t) = 4t – 5; find p(t – 2)
- g(a) = 4a; find g(2a)
- w(n) = 4n + 2; find w(3n)
- w(a) = a + 3; find w(a + 4)
- h(x) = 4x – 2; find h(x + 2)
- k(a) = -4^(3a + 2); find k(a – 2)
- g(n) = n^3 – 5n^2; find g(-4n)
- f(n) = n^2 – 2n; find f(n^2)
- p(a) = a^3 – 5; find p(x – 4)
- h(t) = 2 • 3^(t + 3); find h(4 + t)

## FUNCTION OPERATIONS

- g(n)=n^2+4+2n; h(n)=-3n+2; Find (g•h)(1)
- f(x)=4x-3; g(x)=x^3+2x; Find (f-g)(4)
- h(x)=3x+3; g(x)=-4x+1; Find (h+g)(10)
- g(a)=3a+2; f(a)=2a-4; Find (g/f)(3)
- g(x)=2x-5; h(x)=4x+5; Find g(3)-h(3)
- g(a)=2a-1; h(a)=3a-3; Find (g•h)(-4)
- g(t)=t^2+3; h(t)=4t-3; Find (g•h)(-1)
- g(n)=3n+2; f(n)=2n^2+5; Find g(f(2))
- g(x)=-x^2-1-2x; f(x)=x+5; Find (g-f)(x)
- f(x)=3x-1; g(x)=x^2-x; Find (f/g)(x)
- g(a)=-3a-3; f(a)=a^2+5; Find (g-f)(a)
- h(t)=2t+1; g(t)=2t+2; Find (h-g)(t)
- f(x)=2x^3-5x^2; g(x)=2x-1; Find (f•g)(x)
- h(n)=4n+5; g(n)=3n+4; Find (h-g)(n)
- g(a)=-3a^2-a; h(a)=-2a-4; Find (g/h)(a)
- f(n)=2n; g(n)=-n-4; Find (f o g)(n)
- h(a)=3a; g(a)=-a^3-3; Find (h/g)(a)
- g(n)=2n+3; h(n)=n-1; Find (g o h)(n)
- h(x)=x^2-2; g(x)=4x+1; Find (h o g)(x)
- g(t)=2t+5; f(t)=-t^2+5; Find (g+f)(t)
- g(x)=2x-2; f(x)=x^2+3x; Find (g o f)(-2+x)
- g(a)=2a+2; h(a)=-2a-5; Find (g o h)(-4+a)

## RADICAL FUNCTIONS AND RATIONAL EXPONENTS – 42 Video Lessons

## SIMPLIFYING RATIONAL EXPONENTS

- (n^4)^(3/2)
- (27p^6)^(5/3)
- (25b^6)^(-1.5)
- (64m^4)^(3/2)
- (a^8)^(3/2)
- (9r^4)^0.5
- (81x^12)^1.25
- (216r^9)^(1/3)
- 2m^2•4m^(3/2)•4m^-2
- 3b^(1/2)•b^(4/3)
- (p^(3/2))^-2
- (a^(1/2))^(3/2)
- 2x^(-7/4)/4x^(4/3)
- 4x^2/2x^(1/2)
- (3x^(-1/2)•3x^(1/2)8y^(-1/3))/3y^(-7/4)
- 3y^(1/4)/(4x^(-2/3)•y^(3/2)•3y^(1/2))
- (m•m^-2•n^(5/3))^2
- (a^-1•b^(1/3)•a^(-4/3)•b^2)^2
- ((x^(1/2)•y^-2)/(yx^(-7/4))^4
- (x^3y^2)^(3/2)/(x^-1y^(-2/3))^(1/4)
- (x^(-1/2)y^2)^(-5/4)/(x^2y^(1/2))
- (x^(-1/2)y^4)^(1/4)/(x^(2:3)y^(3/2)*x^(-3/2)y^(1/2))

## RATIONAL EXPONENT EQUATIONS

## RATIONAL EXPRESSIONS – 71 Video Lessons

## SIMPLIFYING RATIONAL EXPRESSIONS

- 60x^3/12x
- 70v^2/100v
- (m+7)/(m^2+4m-21)
- (n^2+6n+5)/(n+1)
- (35x-35)/(25x-40)
- (-n^2+16n-63)/(n^2-2n-35)
- (p+4)/(p^2+6p+8)
- 9/(15a-15)
- (2a^2+10a)/(3a^2+15a)
- (p^2-3p-10)/(p^2+p-2)
- (x^2+x-6)/(x^2+8x+15)
- (a^2+5a+4)/(a^2+9a+20)
- (x^2-2x-15)/(x^2-6x+5)
- (10x-6)/(10x-6)
- (v-7)(v+8)/(v+8)(v-10)÷1/(v-10)
- ((n+3)/(n+2))÷((n-1)(n+3)/(n-1)^2)
- ((x+3)/4)•(3(x-6)/3(x+3))
- ((x-8)/(x+6)(x-8))•(4x(x+10)/(x+10))
- ((2b^2-12b)/(b+5))÷((b-6)/(b+5))
- (1/(n+9))÷((6-n)/(3n-18))
- ((28-7b)/(b-4))•(1/(b+10))
- (2/(v^2-12v+27))•((v^2-12v+27)/3)
- (1/5p^2)÷((9p-36)/(5p^3-35p^2))
- ((8-7x-x^2)/(x+8))•((x+5)/(9x-9))
- ((x^2-16)/(9-x))•((x^2+x-90)/(x^2+14x+40))
- ((10x^2-20x)/(40x^3-80x^2))•((16x^3+80x^2)/(6x+30))

## ADDING/SUBTRACTING RATIONAL EXPRESSIONS

- (u-v)/8v-(6u-3v)/8v
- (m-3n)/6m^3n-(m+3n)/6m^3n
- 5/(a^2+3a+2)+(5a-1)/(a^2+3a+2)
- 5/(10n^2+16n+6)+(n-6)/(10n^2+16n+6)
- (r+6)/(3r-6)+(r+1)/(3r-6)
- (x+2)/(2x^2+13x+20)-(x+3)/(2x^2+13x+20)
- 6/(x-1)-5x/4
- 6-(x+5)/((7x-5)(x+4))
- 3/(x+7)+4/(x-8)
- 3/(4v^2+4v)-7/2
- 7/3-8/(12x-8)
- 5/(n+5)+4n/(2n+6)
- 2x/(5x+4)+6x/(2x+3)
- 2/(3x^2+12x)+8/2x
- 7n/(n+1)+8/(n-7)
- 2/(n+8)+4/(n+1)
- 3/8-3/(3x+4)
- 3/(b-8)+7/(b+3)
- 3/(x+6)+7/(x-2)
- 4/(x+1)-2/(x+2)
- (5n+5)/(5n^2+35n-40)+7n/3n
- 3/(n-5)+6/(3n-8)
- (25/4)/(1/5-4/25)
- 8/(4/9-16/9)
- (a/25-a/5)/a
- (5/4)/(5/m-4/m)
- Simplify: a/b+c/d
- Split into a sum of two rational expressions with unlike denominators: (2x+3)/(x^2+3x+2)

## EXPONENTIAL AND LOGARITHMIC FUNCTIONS – 79 Video Lessons

## LOGARITHMIC EQUATIONS

- log 5x = log(2x+9)
- log(10-4x) = log(10-3x)
- log(4p-2) = log(-5p+5)
- log(4k-5) = log(2k-1)
- log(-2a+9) = log(7-4a)
- 2log_7 – 2r=0
- -10 + log_3 (n+3) = -10
- -2log_5 7x = 2
- log -m + 2 = 4
- -6log_3 (x-3) = -24
- log_12 (v^2+35) = log_12 (-12v-1)
- log_9 (-11x+2) = log_9 (x^2+30)
- log(16+2b) = log(b^2-4b)
- ln(n^2+12) = ln(-9n-2)
- log x + log 8 = 2
- log x – log 2 = 1
- log 2 + log x = 1
- log x + log 7 = 37
- log_8 2 + log_8 4x^2 = 1
- log_9 (x+6) – log_9 x = log_9 2
- log_6 (x+1) – log_6 x = log_6 29
- log_5 6 + log_5 2x^2 = log_5 48
- ln 2 – ln(3x+2) = 1
- ln(-3x-1) – ln 7 = 2
- ln(x-3) – ln(x-5) = ln 5
- ln(4x+1) – ln 3 = 5

## EXPONENTIAL EQUATIONS NOT REQUIRING LOGARITHMS

- 4^(2x+3)=1
- 5^(3-2x)=5^-x
- 3^(1-2x)=243
- 3^2a=3^-a
- 4^(3x-2)=1
- 4^2p=4^(-2p-1)
- 6^-2a=6^(2-3a)
- 2^(2x+2)=2^3x
- 6^3m•6^-m=6^-2m
- 2^x/2^x=2^-2x
- 10^-3x•10^x=1/10
- 3^(-2x+1)•3^(-2x-3)=3^-x
- 4^-2x•4^x=64
- 6^-2x•6^-x=1/216
- 2^x•1/32=16^(3x-2)
- 2^-3p•2^2p=2^2p
- 64•16^-3x=16^(3x-2)
- 81^(3n+2)/243^-n=3^4
- 81•9^(-2b-2)=27
- 9^-3x•9^x=27
- (1/6)^(3x+2)•216^3x=1/216
- 243^(k+2)•9^(2k-1)=9
- 16^r•64^(3-3r)=64
- 16^(2p-3)•4^-2p=2^4

## SOLVING EXPONENTIAL EQUATIONS WITH LOGARITHMS

- 3^b=17
- 12^r=13
- 9^n=49
- 16^v=67
- 3^a=69
- 6^r=51
- 6^n=99
- 20^r=56
- 5•18^6x=26
- e^(x-1)-5=5
- 9^(n+10)+3=81
- 11^(n-8)-5=54
- 16^(n-7)+5=24
- 20^(-6n)+6=55
- 5•6^3m=20
- 8^(-5a)-5=53
- 3.4e^(2-2n)-9=-4
- -6e^(8n+8)-3=-23
- -e^(-3.9n-1)-1=-3
- -2e^(7v+5)-10=-17
- -3e^(7a+9)+6=-6
- -3e^(9x-1)+6=-58
- -e^(6-9p)+5=-48.4
- -10e^(2-2b)-6=-66
- 6e^(-4k-10)-4=63
- 6e^(5x-6)-4=50