Worksheet for factoring trinomial squares with a leading coefficient of 1.

Here are the solutions for each problem on the worksheet. I have factored each trinomial completely.

1) $x^2 + 7x + 6$
Factors of 6 that add to 7 are 6 and 1.
Answer: $(x + 6)(x + 1)$

2) $x^2 - 7x + 6$
Factors of 6 that add to -7 are -6 and -1.
Answer: $(x - 6)(x - 1)$

3) $p^2 - 4p - 45$
Factors of -45 that add to -4 are -9 and 5.
Answer: $(p - 9)(p + 5)$

4) $b^2 - 8b + 12$
Factors of 12 that add to -8 are -6 and -2.
Answer: $(b - 6)(b - 2)$

5) $x^2 - 7x - 8$
Factors of -8 that add to -7 are -8 and 1.
Answer: $(x - 8)(x + 1)$

6) $k^2 + 5k - 5$
There are no integers that multiply to -5 and add to 5. This cannot be factored using integers.
Answer: Prime (or Not Factorable)

7) $a^2 + 14a + 48$
Factors of 48 that add to 14 are 8 and 6.
Answer: $(a + 8)(a + 6)$

8) $n^2 - 15n + 50$
Factors of 50 that add to -15 are -10 and -5.
Answer: $(n - 10)(n - 5)$

9) $p^2 + 4p + 4$
Factors of 4 that add to 4 are 2 and 2.
Answer: $(p + 2)(p + 2)$ or $(p + 2)^2$

10) $x^2 - 6x - 27$
Factors of -27 that add to -6 are -9 and 3.
Answer: $(x - 9)(x + 3)$

11) $r^2 - r + 4$
There are no integers that multiply to 4 and add to -1.
Answer: Prime (or Not Factorable)

12) $x^2 + x - 72$
Factors of -72 that add to 1 are 9 and -8.
Answer: $(x + 9)(x - 8)$

13) $x^2 - 8x - 9$
Factors of -9 that add to -8 are -9 and 1.
Answer: $(x - 9)(x + 1)$

14) $p^2 + 12p + 36$
Factors of 36 that add to 12 are 6 and 6.
Answer: $(p + 6)(p + 6)$ or $(p + 6)^2$

15) $n^2 - 7n - 18$
Factors of -18 that add to -7 are -9 and 2.
Answer: $(n - 9)(n + 2)$

16) $m^2 + 11m + 28$
Factors of 28 that add to 11 are 7 and 4.
Answer: $(m + 7)(m + 4)$

17) $m^2 + 12m + 27$
Factors of 27 that add to 12 are 9 and 3.
Answer: $(m + 9)(m + 3)$

18) $n^2 - 8n - 72$
There are no integers that multiply to -72 and add to -8.
Answer: Prime (or Not Factorable)

19) $v^2 - 4v - 60$
Factors of -60 that add to -4 are -10 and 6.
Answer: $(v - 10)(v + 6)$

20) $v^2 - 4v - 12$
Factors of -12 that add to -4 are -6 and 2.
Answer: $(v - 6)(v + 2)$

21) $u^2 + uv - 6v^2$
We need factors of -6 that add to 1. They are 3 and -2.
Answer: $(u + 3v)(u - 2v)$

22) $x^2 + 4xy - 12y^2$
We need factors of -12 that add to 4. They are 6 and -2.
Answer: $(x + 6y)(x - 2y)$

23) $x^2 + 7xy - 30y^2$
We need factors of -30 that add to 7. They are 10 and -3.
Answer: $(x + 10y)(x - 3y)$

24) $x^2 + 13xy + 36y^2$
We need factors of 36 that add to 13. They are 9 and 4.
Answer: $(x + 9y)(x + 4y)$

25) $x^2 + 9xy + 18y^2$
We need factors of 18 that add to 9. They are 6 and 3.
Answer: $(x + 6y)(x + 3y)$

26) $x^2 - 12xy + 32y^2$
We need factors of 32 that add to -12. They are -8 and -4.
Answer: $(x - 8y)(x - 4y)$

27) $x^2 - 14xy + 48y^2$
We need factors of 48 that add to -14. They are -8 and -6.
Answer: $(x - 8y)(x - 6y)$

28) $x^2 + 3xy - 40y^2$
We need factors of -40 that add to 3. They are 8 and -5.
Answer: $(x + 8y)(x - 5y)$

29) $m^2 - 7mn - 8n^2$
We need factors of -8 that add to -7. They are -8 and 1.
Answer: $(m - 8n)(m + n)$

30) $x^2 - 8xy + 7y^2$
We need factors of 7 that add to -8. They are -7 and -1.
Answer: $(x - 7y)(x - y)$

31) $x^2 + 2xy + 4y^2$
There are no integers that multiply to 4 and add to 2.
Answer: Prime (or Not Factorable)

32) $a^2 + 4ab - 5b^2$
We need factors of -5 that add to 4. They are 5 and -1.
Answer: $(a + 5b)(a - b)$

33) $x^2 + 12xy + 32y^2$
We need factors of 32 that add to 12. They are 8 and 4.
Answer: $(x + 8y)(x + 4y)$

34) $c^2 + 9cy + 14y^2$
We need factors of 14 that add to 9. They are 7 and 2.
Answer: $(c + 7y)(c + 2y)$

35) $u^2 - 12uv + 20v^2$
We need factors of 20 that add to -12. They are -10 and -2.
Answer: $(u - 10v)(u - 2v)$

36) $u^2 - uv - 2v^2$
We need factors of -2 that add to -1. They are -2 and 1.
Answer: $(u - 2v)(u + v)$

37) $x^2 + 2xy + 12y^2$
There are no integers that multiply to 12 and add to 2.
Answer: Prime (or Not Factorable)

38) $m^2 + 13mn + 40n^2$
We need factors of 40 that add to 13. They are 8 and 5.
Answer: $(m + 8n)(m + 5n)$

39) $u^2 + 8uv + 12v^2$
We need factors of 12 that add to 8. They are 6 and 2.
Answer: $(u + 6v)(u + 2v)$

40) $x^2 + 10xy + 16y^2$
We need factors of 16 that add to 10. They are 8 and 2.
Answer: $(x + 8y)(x + 2y)$