Solving quadratic equations by factoring - Kuta Software

Kuta Software - Infinite Algebra 2

Name___________________________________

Solving Quadratic Equations By Factoring

Date________________ Period____

Solve each equation by factoring. 1) (3n − 2)(4n + 1) = 0

2) m(m − 3) = 0

3) (5n − 1)(n + 1) = 0

4) (n + 2)(2n + 5) = 0

5) 3k 2 + 72 = 33k

6) n 2 = −18 − 9n

7) 7v 2 − 42 = −35v

8) k 2 = −4k − 4

9) −2v 2 − v + 12 = −3v 2 + 6v

10) −4n 2 + 6n − 16 = −5n 2

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Worksheet by Kuta Software LLC

11) 8r 2 + 3r + 2 = 7r 2

12) b 2 + b = 2

13) 10n 2 − 35 = 65n

14) 3 x 2 − 8 x = 16

15) 16n 2 − 114n = −14

16) 28n 2 = −96 − 184n

17) 7a 2 + 32 = 7 − 40a

18) 42 x 2 − 69 x + 20 = 7 x 2 − 8

Critical thinking questions. True/False. 19) If a quadratic equation can be factored and each factor contains only real numbers then there cannot be an imaginary solution.

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20) If a quadratic equation cannot be factored then it will have at least one imaginary solution.

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Kuta Software - Infinite Algebra 2

Name___________________________________

Solving Quadratic Equations By Factoring

Date________________ Period____

Solve each equation by factoring. 1) (3n − 2)(4n + 1) = 0

2) m(m − 3) = 0

{3, 0}

{ } 2 1 ,− 3 4

3) (5n − 1)(n + 1) = 0

4) (n + 2)(2n + 5) = 0

{ }

{

1 , −1 5

5) 3k 2 + 72 = 33k

−2, −

{−6, −3}

8) k 2 = −4k − 4

{−2}

{−6, 1}

9) −2v 2 − v + 12 = −3v 2 + 6v

10) −4n 2 + 6n − 16 = −5n 2

{3, 4}

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}

6) n 2 = −18 − 9n

{3, 8}

7) 7v 2 − 42 = −35v

5 2

{2, −8}

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11) 8r 2 + 3r + 2 = 7r 2

12) b 2 + b = 2

{−2, −1}

{−2, 1}

13) 10n 2 − 35 = 65n

14) 3 x 2 − 8 x = 16

{ }

{ }

1 − ,7 2

4 − ,4 3

15) 16n 2 − 114n = −14

16) 28n 2 = −96 − 184n

{ }

{

4 − , −6 7

1 ,7 8

17) 7a 2 + 32 = 7 − 40a

{

5 − , −5 7

}

18) 42 x 2 − 69 x + 20 = 7 x 2 − 8

}

{ } 7 4 , 5 7

Critical thinking questions. True/False. 19) If a quadratic equation can be factored and each factor contains only real numbers then there cannot be an imaginary solution.

20) If a quadratic equation cannot be factored then it will have at least one imaginary solution. False (Example, x 2 = 10)

True Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com

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