FACTORING QUADRATIC TRINOMIALS WORKSHEET

Problems 1-12 : Write each quadratic trinomial in factored form (as the product of two binomials).

Problem 1 :

x² + 14x + 48

Problem 2 :

y² + 10y + 16

Problem 3 :

m² + 14m + 40

Problem 4 :

k² + 9k + 18

Problem 5 :

n² - 8n + 7

Problem 6 :

a² - 9a + 14

Problem 7 :

c² - 8c + 15

Problem 8 :

x² - 16m + 63

Problem 9 :

y² - 4y - 60

Problem 10 :

k² + k - 6

Problem 11 :

p² - 2p - 15

Problem 12 :

r² + r - 20

Problems 13-18 : Factor each completely. (Remember to pull out the greatest common factor first.)

Problem 13 :

3x² + 21x + 30

Problem 14 :

2y² + 14y + 24

Problem 15 :

2m² - 16m + 30

Problem 16 :

3k² - 9k + 6

Problem 17 :

3n² - 3n - 36

Problem 18 :

2a² + 2a - 12

Answers

1. Answer :

= x² + 14x + 48

= x² + 8x + 6x + 48

= x(x + 8) + 6(x + 8)

= (x + 8)(x + 6)

2. Answer :

= y² + 10y + 16

= y² + 8y + 2y + 16

= y(y + 8) + 2(y + 8)

= (y + 8)(y + 2)

3. Answer :

= m² + 14m + 40

= m² + 10m + 4m + 40

= m(m + 10) + 4(m + 10)

= (m + 10)(m + 4)

4. Answer :

= k² + 9k + 18

= k² + 6k + 3k + 18

= k(k + 6) + 3(k + 6)

= (k + 6)(k + 3)

5. Answer :

= n² - 8n + 7

= n² - 7n - 1n + 7

= n(n - 7) - 1(n - 7)

= (n - 7)(n - 1)

6. Answer :

= a² - 9a + 14

= a² - 7a - 2a + 14

= a(a - 7) - 2(a - 7)

= (a - 7)(a - 2)

7. Answer :

= c² - 8c + 15

= c² - 5c - 3c + 15

= c(c - 5) - 3(c - 5)

= (c - 5)(c - 3)

8. Answer :

= m² - 16m + 63

= m² - 9m - 7m + 63

= m(m - 9) - 7(m - 9)

= (m - 9)(m - 7)

9. Answer :

= y² - 4y - 60

= y² - 10y + 6y - 60

= y(y - 10) + 6(y - 10)

= (y - 10)(y + 6)

10. Answer :

= k² + k - 6

= k² + 3k - 2k - 6

= k(k + 3) - 2(k + 3)

= (k + 3)(k - 2)

11. Answer :

= p² - 2p - 15

= p² - 5p + 3p - 15

= p(p - 5) + 3(p - 5)

= (p - 5)(p + 3)

12. Answer :

= r² + r - 20

= r² + 5r - 4r - 20

= r(r + 5) - 4(r + 5)

= (r + 5)(r - 4)

13. Answer :

= 3x² + 21x + 30

= 3(x² + 7x + 10)

= 3(x² + 5x + 2x + 10)

= 3[x(x + 5) + 2(x + 5)]

= 3(x + 5)(x + 2)

14. Answer :

= 2y² + 14y + 24

= 2(y² + 7y + 12)

= 2(y² + 4y + 3y + 12)

= 2[y(y + 4) + 3(y + 4)]

= 2(y + 4)(y + 3)

15. Answer :

= 2m² - 16m + 30

= 2(m² - 8m + 15)

= 2(m² - 5m - 3m + 15)

= 2[m(m - 5) - 3(m - 5)]

= 2(m - 5)(m - 3)

16. Answer :

= 3k² - 9k + 6

= 3(k² - 3k + 2)

= 3(k² - 2k - 1k + 2)

= 3[k(k - 2) - 1(k - 2)]

= 3(k - 2)(k - 1)

17. Answer :

= 3n² - 3n - 36

= 3(n² - n - 12)

= 3(n² - 4n + 3n - 12)

= 3[n(n - 4) + 3(n - 4)]

= 3(n - 4)(n + 3)

18. Answer :

= 2a² + 2a - 12

= 2(a² + a - 6)

= 2(a² + 3a - 2a - 6)

= 2[a(a + 3) - 2(a + 3)]

= 2(a + 3)(a - 2)

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