Solving Quadratics by Factoring

Question 1

Solve 6x^2 - 5 = -13x by factoring.

Accepted Answer

x = -5/2 or x = 1/3

Answer

x = -1/3 or x = 5/2

Answer

x = -2/5 or x = 3

Answer

x = -5/2 or x = -1/3

Question 2

Solve 5x^2 + 16 = -24x by factoring.

Accepted Answer

x = -4 or x = -4/5

Answer

x = 4/5 or x = 4

Answer

x = -5/4 or x = -1/4

Answer

x = -4/5 or x = 4

Question 3

To solve (x - 2)(x + 4) = 27, a student set x - 2 = 27 and x + 4 = 27 and answered x = 29 or x = 23. What are the actual solutions?

Accepted Answer

x = -7 or x = 5

Answer

x = 23 or x = 29

Answer

x = -4 or x = 2

Answer

x = -5 or x = 7

Question 4

Solve 10x^2 + 7x - 12 = 0 by factoring.

Accepted Answer

x = -3/2 or x = 4/5

Answer

x = -4/5 or x = 3/2

Answer

x = -2/3 or x = 5/4

Answer

x = -3/2 or x = -4/5

Question 5

Solve 4x^2 + 13x - 12 = 0 by factoring.

Accepted Answer

x = -4 or x = 3/4

Answer

x = -3/4 or x = 4

Answer

x = -1/4 or x = 4/3

Answer

x = -4 or x = -3/4

Question 6

Solve 3x^2 - 4x - 15 = 0 by factoring.

Accepted Answer

x = -5/3 or x = 3

Answer

x = -3 or x = 5/3

Answer

x = -3/5 or x = 1/3

Answer

x = 5/3 or x = 3

Question 7

To solve (x - 2)(x + 6) = 9, a student set x - 2 = 9 and x + 6 = 9 and answered x = 11 or x = 3. What are the actual solutions?

Accepted Answer

x = -7 or x = 3

Answer

x = 3 or x = 11

Answer

x = -6 or x = 2

Answer

x = -3 or x = 7

Question 8

One solution of 4x^2 + bx - 6 = 0 is x = -3/2. What is the value of b?

Accepted Answer

b = 2

Answer

b = -2

Answer

b = 8

Answer

b = -8

Question 9

To solve (x - 1)(x + 6) = 44, a student set x - 1 = 44 and x + 6 = 44 and answered x = 45 or x = 38. What are the actual solutions?

Accepted Answer

x = -10 or x = 5

Answer

x = 38 or x = 45

Answer

x = -6 or x = 1

Answer

x = -5 or x = 10

Question 10

One solution of 2x^2 + bx - 15 = 0 is x = 5/2. What is the value of b?

Accepted Answer

b = 1

Answer

b = -1

Answer

b = 7

Answer

b = -7

Question 11

Solve 2x^2 - 3x - 20 = 0 by factoring.

Accepted Answer

x = -5/2 or x = 4

Answer

x = -4 or x = 5/2

Answer

x = -2/5 or x = 1/4

Answer

x = 5/2 or x = 4

Question 12

Solve 5x^2 - 2 = 3x by factoring.

Accepted Answer

x = -2/5 or x = 1

Answer

x = -1 or x = 2/5

Answer

x = -5/2 or x = 1

Answer

x = -1 or x = -2/5

Question 13

To solve (x - 1)(x + 3) = 5, a student set x - 1 = 5 and x + 3 = 5 and answered x = 6 or x = 2. What are the actual solutions?

Accepted Answer

x = -4 or x = 2

Answer

x = 2 or x = 6

Answer

x = -3 or x = 1

Answer

x = -2 or x = 4

Question 14

Solve x^4 - 52x^2 + 576 = 0 by factoring.

Accepted Answer

x = -6, -4, 4 or 6

Answer

x = -36, -16, 16 or 36

Answer

x = -6, -4, 16 or 36

Answer

x = 4 or x = 6

Question 15

One solution of 4x^2 + bx - 12 = 0 is x = -3/2. What is the value of b?

Accepted Answer

b = -2

Answer

b = 2

Answer

b = 4

Answer

b = -4

Question 16

Solve 2x^2 - 6 = -11x by factoring.

Accepted Answer

x = -6 or x = 1/2

Answer

x = -1/2 or x = 6

Answer

x = -1/6 or x = 2

Answer

x = -6 or x = -1/2

Question 17

To solve (x - 1)(x + 6) = 8, a student set x - 1 = 8 and x + 6 = 8 and answered x = 9 or x = 2. What are the actual solutions?

Accepted Answer

x = -7 or x = 2

Answer

x = 2 or x = 9

Answer

x = -6 or x = 1

Answer

x = -2 or x = 7

Question 18

Solve x^4 - 25x^2 + 144 = 0 by factoring.

Accepted Answer

x = -4, -3, 3 or 4

Answer

x = -16, -9, 9 or 16

Answer

x = -4, -3, 9 or 16

Answer

x = 3 or x = 4

Question 19

Solve x^4 - 10x^2 + 9 = 0 by factoring.

Accepted Answer

x = -3, -1, 1 or 3

Answer

x = -9, -1, 1 or 9

Answer

x = -3, -1, 1 or 9

Answer

x = 1 or x = 3

Question 20

Solve 15x^2 + x - 6 = 0 by factoring.

Accepted Answer

x = -2/3 or x = 3/5

Answer

x = -3/5 or x = 2/3

Answer

x = -3/2 or x = 5/3

Answer

x = -2/3 or x = -3/5

Question 21

Solve 3x^2 + 14x - 24 = 0 by factoring.

Accepted Answer

x = -6 or x = 4/3

Answer

x = -4/3 or x = 6

Answer

x = -1/6 or x = 3/4

Answer

x = 4/3 or x = 6

Question 22

One solution of 2x^2 + bx - 15 = 0 is x = 3/2. What is the value of b?

Accepted Answer

b = 7

Answer

b = -7

Answer

b = 13

Answer

b = -13

Question 23

Solve 3x^2 - 7x - 20 = 0 by factoring.

Accepted Answer

x = -5/3 or x = 4

Answer

x = -4 or x = 5/3

Answer

x = -3/5 or x = 1/4

Answer

x = 5/3 or x = 4

Question 24

Solve 4x^2 + x - 5 = 0 by factoring.

Accepted Answer

x = -5/4 or x = 1

Answer

x = -1 or x = 5/4

Answer

x = -4/5 or x = 1

Answer

x = 1 or x = 5/4

Question 25

Solve 15x^2 - 13x + 2 = 0 by factoring.

Accepted Answer

x = 1/5 or x = 2/3

Answer

x = -2/3 or x = -1/5

Answer

x = 3/2 or x = 5

Answer

x = -1/5 or x = 2/3

Question 26

Solve 10x^2 + 9x - 9 = 0 by factoring.

Accepted Answer

x = -3/2 or x = 3/5

Answer

x = -3/5 or x = 3/2

Answer

x = -2/3 or x = 5/3

Answer

x = -3/2 or x = -3/5

Question 27

One solution of 2x^2 + bx + 6 = 0 is x = -1/2. What is the value of b?

Accepted Answer

b = 13

Answer

b = -13

Answer

b = 19

Answer

b = -19

Question 28

Solve x^4 - 61x^2 + 900 = 0 by factoring.

Accepted Answer

x = -6, -5, 5 or 6

Answer

x = -36, -25, 25 or 36

Answer

x = -6, -5, 25 or 36

Answer

x = 5 or x = 6

Question 29

Solve x^4 - 29x^2 + 100 = 0 by factoring.

Accepted Answer

x = -5, -2, 2 or 5

Answer

x = -25, -4, 4 or 25

Answer

x = -5, -2, 4 or 25

Answer

x = 2 or x = 5

Question 30

Solve 5x^2 + 11x + 6 = 0 by factoring.

Accepted Answer

x = -6/5 or x = -1

Answer

x = 1 or x = 6/5

Answer

x = -1 or x = -5/6

Answer

x = -1 or x = 6/5

Question 31

Solve x^4 - 5x^2 + 4 = 0 by factoring.

Accepted Answer

x = -2, -1, 1 or 2

Answer

x = -4, -1, 1 or 4

Answer

x = -2, -1, 1 or 4

Answer

x = 1 or x = 2

Question 32

One solution of 4x^2 + bx - 15 = 0 is x = -5/2. What is the value of b?

Accepted Answer

b = 4

Answer

b = -4

Answer

b = 10

Answer

b = -10

Question 33

Solve 2x^2 - 12 = 5x by factoring.

Accepted Answer

x = -3/2 or x = 4

Answer

x = -4 or x = 3/2

Answer

x = -2/3 or x = 1/4

Answer

x = -4 or x = -3/2

Question 34

Solve 10x^2 + 3 = -17x by factoring.

Accepted Answer

x = -3/2 or x = -1/5

Answer

x = 1/5 or x = 3/2

Answer

x = -5 or x = -2/3

Answer

x = -1/5 or x = 3/2

Question 35

Solve x^4 - 26x^2 + 25 = 0 by factoring.

Accepted Answer

x = -5, -1, 1 or 5

Answer

x = -25, -1, 1 or 25

Answer

x = -5, -1, 1 or 25

Answer

x = 1 or x = 5

Question 36

To solve (x - 2)(x + 1) = 18, a student set x - 2 = 18 and x + 1 = 18 and answered x = 20 or x = 17. What are the actual solutions?

Accepted Answer

x = -4 or x = 5

Answer

x = 17 or x = 20

Answer

x = -1 or x = 2

Answer

x = -5 or x = 4

Question 37

Solve 2x^2 - 15 = -x by factoring.

Accepted Answer

x = -3 or x = 5/2

Answer

x = -5/2 or x = 3

Answer

x = -1/3 or x = 2/5

Answer

x = 5/2 or x = 3

Question 38

Solve 6x^2 + 5 = 13x by factoring.

Accepted Answer

x = 1/2 or x = 5/3

Answer

x = -5/3 or x = -1/2

Answer

x = 3/5 or x = 2

Answer

x = -5/3 or x = 1/2

Question 39

Solve 3x^2 - 20x + 25 = 0 by factoring.

Accepted Answer

x = 5/3 or x = 5

Answer

x = -5 or x = -5/3

Answer

x = 1/5 or x = 3/5

Answer

x = -5/3 or x = 5

Question 40

Solve x^4 - 45x^2 + 324 = 0 by factoring.

Accepted Answer

x = -6, -3, 3 or 6

Answer

x = -36, -9, 9 or 36

Answer

x = -6, -3, 9 or 36

Answer

x = 3 or x = 6

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Solving Quadratics by Factoring

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Solving Quadratics by Factoring

Ways to Play

Device Games: Students play on their phones

Blast Go

Zombie Escape

Avalanche

Maze Blast

Cave Climb

Blast Out

Mystery Auction

Tour Guide

Food Truck Rush

Tug of War

Alien Blast

Glacier Rush

Board Games: Teacher-led, projected to the class

Like what you see?

More like this

Bug Blast

BlastRace

BlastQuiz

BlastBoard

Seek & Destroy

Mystery Blast

Checkers

Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner