3.1 Factoring Quadratic Expressions

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Kuta Software - Infinite Algebra 2

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Factoring Quadratic Expressions

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Factor each completely. 1) x 2 − 7 x − 18

2) p 2 − 5 p − 14

3) m 2 − 9m + 8

4) x 2 − 16 x + 63

5) 7 x 2 − 31 x − 20

6) 7k 2 + 9k

7) 7 x 2 − 45 x − 28

8) 2b 2 + 17b + 21

9) 5 p 2 − p − 18

10) 28n 4 + 16n 3 − 80n 2

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11) 3b 3 − 5b 2 + 2b

12) 7 x 2 − 32 x − 60

13) 30n 2 b − 87nb + 30b

14) 9r 2 − 5r − 10

15) 9 p 2 r + 73 pr + 70r

16) 9 x 2 + 7 x − 56

17) 4 x 3 + 43 x 2 + 30 x

18) 10m 2 + 89m − 9

Critical thinking questions: 19) For what values of b is the expression factorable? x 2 + bx + 12

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20) Name four values of b which make the expression factorable: x2 − 3x + b

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Worksheet by Kuta Software LLC

Kuta Software - Infinite Algebra 2

Name___________________________________

Factoring Quadratic Expressions

Date________________ Period____

Factor each completely. 1) x 2 − 7 x − 18

2) p 2 − 5 p − 14

( x − 9)( x + 2)

3) m 2 − 9m + 8

( p + 2)( p − 7)

4) x 2 − 16 x + 63

(m − 1)(m − 8)

5) 7 x 2 − 31 x − 20

( x − 9)( x − 7)

6) 7k 2 + 9k

(7 x + 4)( x − 5)

7) 7 x 2 − 45 x − 28

k(7k + 9)

8) 2b 2 + 17b + 21

(7 x + 4)( x − 7)

9) 5 p 2 − p − 18

(2b + 3)(b + 7)

10) 28n 4 + 16n 3 − 80n 2

(5 p + 9)( p − 2)

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4n 2 (7n − 10)(n + 2)

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11) 3b 3 − 5b 2 + 2b

12) 7 x 2 − 32 x − 60

b(3b − 2)(b − 1)

13) 30n 2 b − 87nb + 30b

(7 x + 10)( x − 6)

14) 9r 2 − 5r − 10

3b(2n − 5)(5n − 2)

15) 9 p 2 r + 73 pr + 70r

Not factorable

16) 9 x 2 + 7 x − 56

r( p + 7)(9 p + 10)

17) 4 x 3 + 43 x 2 + 30 x

Not factorable

18) 10m 2 + 89m − 9

x( x + 10)(4 x + 3)

(m + 9)(10m − 1)

Critical thinking questions: 19) For what values of b is the expression factorable? x 2 + bx + 12

20) Name four values of b which make the expression factorable: x2 − 3x + b

13, 8, 7, −13, −8, −7

Many answers. Ex: 0, 2, −4, −10, −18

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Worksheet by Kuta Software LLC