FACTORING TRINOMIALS WORKSHEET

Factor each trinomial completely.

Problem 1 :

x² + 8x + 7

Problem 2 :

m² - 11m + 10

Problem 3 :

y² + y - 90

Problem 4 :

r² + 4r - 12

Problem 5 :

p² - 10p + 9

Problem 6 :

z² + 16z + 64

Problem 7 :

x² + 2x - 24

Problem 8 :

y² - 4y - 12

Problem 9 :

a² - 13a + 40

Problem 10 :

d² + 11d + 18

Problem 11 :

2x² + 6x - 108

Problem 12 :

3k² + 6k - 9

Problem 13 :

5w² - 30w + 40

Problem 14 :

3x² - 2x - 5

Problem 15 :

2m² + 3m - 9

Problem 16 :

9y² + 66y + 21

Answers

1. Answer :

= x² + 8x + 7

= x² + 7x + 1x + 7

= x(x + 7) + 1(x + 7)

= (x + 7)(x + 1)

2. Answer :

= m² - 11m + 10

= m² - 10m - 1m + 10

= m(m - 10) - 1(m - 10)

= (m - 10)(m - 1)

3. Answer :

= y² + y - 90

= y² + 10y - 9y - 90

= y(y + 10) - 9(y + 10)

= (y + 10)(y - 9)

4. Answer :

= r² + 4r - 12

= r² + 6r - 2r - 12

= r(r + 6) - 2(r + 6)

= (r + 6)(r - 2)

5. Answer :

= p² - 10p + 9

= p² - 9p - 1p + 9

= p(p - 9) - 1(p - 9)

= (p - 9)(p - 1)

6. Answer :

= z² + 16z + 64

= z² + 8z + 8z + 64

= z(z + 8) + 8(z + 8)

= (z + 8)(z + 8)

7. Answer :

= x² + 2x - 24

= x² + 6x - 4x - 24

= x(x + 6) - 4(x + 6)

= (x + 6)(x - 4)

8. Answer :

= y² - 4y - 12

= y² - 6y + 2y - 12

= y(y - 6) + 2(y - 6)

= (y - 6)(y + 2)

9. Answer :

= a² - 13a + 40

= a² - 8a - 5a + 40

= a(a - 8) - 5(a - 8)

= (a - 8)(a - 5)

10. Answer :

= d² + 11d + 18

= d² + 9d + 2d + 18

= d(d + 9) + 2(d + 9)

= (d + 9)(d + 2)

11. Answer :

= 2x² + 6x - 108

= 2(x² + 3x - 54)

= 2(x² + 9x - 6x - 54)

= 2[x(x + 9) - 6(x + 9)]

= 2(x + 9)(x - 6)

12. Answer :

= 3k² + 6k - 9

= 3(k² + 2k - 3)

= 3(k² + 3k - 1k - 3)

= 3[k(k + 3) - 1(k + 3)]

= 3(k + 3)(k - 1)

13. Answer :

= 5w² - 30w + 40

= 5(w² - 6w + 8)

= 5(w² - 4w - 2w + 8)

= 5[w(w - 4) - 2(w - 4)]

= 5(w - 4)(w - 2)

14. Answer :

= 3x² - 2x - 5

= 3x² - 5x + 3x - 5

= x(3x - 5) + 1(3x - 5)

= (3x - 5)(x + 1)

15. Answer :

= 2m² + 3m - 9

= 2m² + 6m - 3m - 9

= 2m(m - 3) - 3(m - 3)

= (m - 3)(2m - 3)

16. Answer :

= 9y² + 66y + 21

= 3(3y² + 22y + 7)

= 3(3y² + 21y + 1y + 7)

= 3[(3(y + 7) + 1(y + 7)]

= 3(y + 7)(3y + 1)

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