Factoring

Taking out a common factor, the difference of two squares, and factoring x² + bx + c.

6 sheets · 60 questions · one answer key · 9 pages

Recommended for grades 8–9

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Common factor: two terms Sheet 1 of 6

Taking out a common factorTwo terms

Name: Date:

Take out the greatest common factor. Fill in every number.

119x + 228

224x + 2

336x + 162

448x + 6

540x + 32

684x + 49

7156x + 13

842x + 66

966x + 154

10264x + 144

Taking out a common factorThree terms

Name: Date:

Take out the greatest common factor. Fill in every number.

18x² + 32x + 24

222x² + 44x + 66

324x² + 32x + 64

480x² + 140x + 120

599x² + 132x + 22

633x² + 3x + 21

772x² + 42x + 54

870x² + 70x + 14

946x² + 276x + 69

10126x² + 252x + 147

Difference of two squaresX² minus a square

Name: Date:

Each one is a difference of two squares. Factor it.

1x² − 1225

2x² − 1089

3x² − 289

4x² − 256

5x² − 36

6x² − 16

7x² − 25

8x² − 49

9x² − 196

10x² − 4

Factoring quadraticsBoth numbers positive

Name: Date:

Factor each one.

1x² + 28x + 171

2x² + 17x + 60

3x² + 31x + 240

4x² + 16x + 39

5x² + 24x + 23

6x² + 45x + 506

7x² + 18x + 81

8x² + 25x + 136

9x² + 30x + 189

10x² + 6x + 9

Factoring quadraticsBoth numbers negative

Name: Date:

Factor each one. Both numbers are negative.

1x² − 28x + 160

2x² − 29x + 120

3x² − 17x + 16

4x² − 20x + 99

5x² − 22x + 121

6x² − 36x + 323

7x² − 26x + 169

8x² − 34x + 285

9x² − 46x + 529

10x² − 15x + 54

Factoring quadraticsOne positive, one negative

Name: Date:

Factor each one. The two numbers have opposite signs.

1x² + 8x − 308

2x² − 14x − 51

3x² − 15x − 100

4x² + 3x − 504

5x² − 10x − 56

6x² − 10x − 75

7x² + 4x − 77

8x² + 11x − 242

9x² + 17x − 110

10x² − 16x − 57

Power Pack · FactoringAnswer key

Common factor: two terms

1. 19x + 228 = 19(x + 12) (19 ÷ 19 = 1, 228 ÷ 19 = 12)2. 24x + 2 = 2(12x + 1) (24 ÷ 2 = 12, 2 ÷ 2 = 1)3. 36x + 162 = 18(2x + 9) (36 ÷ 18 = 2, 162 ÷ 18 = 9)4. 48x + 6 = 6(8x + 1) (48 ÷ 6 = 8, 6 ÷ 6 = 1)5. 40x + 32 = 8(5x + 4) (40 ÷ 8 = 5, 32 ÷ 8 = 4)6. 84x + 49 = 7(12x + 7) (84 ÷ 7 = 12, 49 ÷ 7 = 7)7. 156x + 13 = 13(12x + 1) (156 ÷ 13 = 12, 13 ÷ 13 = 1)8. 42x + 66 = 6(7x + 11) (42 ÷ 6 = 7, 66 ÷ 6 = 11)9. 66x + 154 = 22(3x + 7) (66 ÷ 22 = 3, 154 ÷ 22 = 7)10. 264x + 144 = 24(11x + 6) (264 ÷ 24 = 11, 144 ÷ 24 = 6)

Common factor: three terms

1. 8x² + 32x + 24 = 8(x² + 4x + 3) (8 ÷ 8 = 1, 32 ÷ 8 = 4, 24 ÷ 8 = 3)2. 22x² + 44x + 66 = 22(x² + 2x + 3) (22 ÷ 22 = 1, 44 ÷ 22 = 2, 66 ÷ 22 = 3)3. 24x² + 32x + 64 = 8(3x² + 4x + 8) (24 ÷ 8 = 3, 32 ÷ 8 = 4, 64 ÷ 8 = 8)4. 80x² + 140x + 120 = 20(4x² + 7x + 6) (80 ÷ 20 = 4, 140 ÷ 20 = 7, 120 ÷ 20 = 6)5. 99x² + 132x + 22 = 11(9x² + 12x + 2) (99 ÷ 11 = 9, 132 ÷ 11 = 12, 22 ÷ 11 = 2)6. 33x² + 3x + 21 = 3(11x² + x + 7) (33 ÷ 3 = 11, 3 ÷ 3 = 1, 21 ÷ 3 = 7)7. 72x² + 42x + 54 = 6(12x² + 7x + 9) (72 ÷ 6 = 12, 42 ÷ 6 = 7, 54 ÷ 6 = 9)8. 70x² + 70x + 14 = 14(5x² + 5x + 1) (70 ÷ 14 = 5, 70 ÷ 14 = 5, 14 ÷ 14 = 1)9. 46x² + 276x + 69 = 23(2x² + 12x + 3) (46 ÷ 23 = 2, 276 ÷ 23 = 12, 69 ÷ 23 = 3)10. 126x² + 252x + 147 = 21(6x² + 12x + 7) (126 ÷ 21 = 6, 252 ÷ 21 = 12, 147 ÷ 21 = 7)

Difference of squares

1. x² − 1225 = (x + 35)(x − 35) (1225 is 35 squared, so the two brackets are (x + 35) and (x − 35))2. x² − 1089 = (x + 33)(x − 33) (1089 is 33 squared, so the two brackets are (x + 33) and (x − 33))3. x² − 289 = (x + 17)(x − 17) (289 is 17 squared, so the two brackets are (x + 17) and (x − 17))4. x² − 256 = (x + 16)(x − 16) (256 is 16 squared, so the two brackets are (x + 16) and (x − 16))

Power Pack · FactoringAnswer key

Difference of squares

5. x² − 36 = (x + 6)(x − 6) (36 is 6 squared, so the two brackets are (x + 6) and (x − 6))6. x² − 16 = (x + 4)(x − 4) (16 is 4 squared, so the two brackets are (x + 4) and (x − 4))7. x² − 25 = (x + 5)(x − 5) (25 is 5 squared, so the two brackets are (x + 5) and (x − 5))8. x² − 49 = (x + 7)(x − 7) (49 is 7 squared, so the two brackets are (x + 7) and (x − 7))9. x² − 196 = (x + 14)(x − 14) (196 is 14 squared, so the two brackets are (x + 14) and (x − 14))10. x² − 4 = (x + 2)(x − 2) (4 is 2 squared, so the two brackets are (x + 2) and (x − 2))

Quadratics: both positive

1. x² + 28x + 171 = (x + 19)(x + 9) (19 and 9)2. x² + 17x + 60 = (x + 5)(x + 12) (5 and 12)3. x² + 31x + 240 = (x + 15)(x + 16) (15 and 16)4. x² + 16x + 39 = (x + 13)(x + 3) (13 and 3)5. x² + 24x + 23 = (x + 1)(x + 23) (1 and 23)6. x² + 45x + 506 = (x + 23)(x + 22) (23 and 22)7. x² + 18x + 81 = (x + 9)(x + 9) (9 and 9)8. x² + 25x + 136 = (x + 17)(x + 8) (17 and 8)9. x² + 30x + 189 = (x + 21)(x + 9) (21 and 9)10. x² + 6x + 9 = (x + 3)(x + 3) (3 and 3)

Quadratics: both negative

1. x² − 28x + 160 = (x − 8)(x − 20) (−8 and −20)2. x² − 29x + 120 = (x − 24)(x − 5) (−24 and −5)3. x² − 17x + 16 = (x − 16)(x − 1) (−16 and −1)4. x² − 20x + 99 = (x − 9)(x − 11) (−9 and −11)5. x² − 22x + 121 = (x − 11)(x − 11) (−11 and −11)6. x² − 36x + 323 = (x − 17)(x − 19) (−17 and −19)7. x² − 26x + 169 = (x − 13)(x − 13) (−13 and −13)8. x² − 34x + 285 = (x − 15)(x − 19) (−15 and −19)9. x² − 46x + 529 = (x − 23)(x − 23) (−23 and −23)10. x² − 15x + 54 = (x − 6)(x − 9) (−6 and −9)

Quadratics: opposite signs

1. x² + 8x − 308 = (x + 22)(x − 14) (22 and −14)2. x² − 14x − 51 = (x + 3)(x − 17) (3 and −17)3. x² − 15x − 100 = (x − 20)(x + 5) (−20 and 5)4. x² + 3x − 504 = (x + 24)(x − 21) (24 and −21)

Power Pack · FactoringAnswer key

Quadratics: opposite signs

5. x² − 10x − 56 = (x − 14)(x + 4) (−14 and 4)6. x² − 10x − 75 = (x − 15)(x + 5) (−15 and 5)7. x² + 4x − 77 = (x − 7)(x + 11) (−7 and 11)8. x² + 11x − 242 = (x + 22)(x − 11) (22 and −11)9. x² + 17x − 110 = (x + 22)(x − 5) (22 and −5)10. x² − 16x − 57 = (x − 19)(x + 3) (−19 and 3)

Factoring

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