Factoring Trinomials worksheet with 30 problems for practice.

Here are the factored forms for each trinomial on the worksheet.

1) $x^2 + 11x + 18$
Factors of 18 that add to 11 are 9 and 2.
Answer: $(x + 9)(x + 2)$

2) $x^2 + 2x - 99$
Factors of -99 that add to 2 are 11 and -9.
Answer: $(x + 11)(x - 9)$

3) $x^2 - 2x - 35$
Factors of -35 that add to -2 are -7 and 5.
Answer: $(x - 7)(x + 5)$

4) $-2x^2 - 11x - 9$
First, factor out the negative sign: $-(2x^2 + 11x + 9)$.
Inside the parenthesis, we need factors of $2 \cdot 9 = 18$ that add to 11. Those are 9 and 2.
Split the middle term: $2x^2 + 9x + 2x + 9$.
Group: $x(2x + 9) + 1(2x + 9)$.
Result inside is $(2x + 9)(x + 1)$. Don't forget the negative sign outside.
Answer: $-(2x + 9)(x + 1)$

5) $x^2 - 1x - 20$
Factors of -20 that add to -1 are -5 and 4.
Answer: $(x - 5)(x + 4)$

6) $x^2 - 64$
This is a difference of squares ($a^2 - b^2$). $\sqrt{64} = 8$.
Answer: $(x - 8)(x + 8)$

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

8) $x^2 + 9x + 14$
Factors of 14 that add to 9 are 7 and 2.
Answer: $(x + 7)(x + 2)$

9) $4x^2 + 3x - 7$
Multiply $a \cdot c$: $4 \cdot -7 = -28$. Find factors of -28 that add to 3. They are 7 and -4.
Rewrite middle term: $4x^2 - 4x + 7x - 7$.
Factor by grouping: $4x(x - 1) + 7(x - 1)$.
Answer: $(4x + 7)(x - 1)$

10) $x^2 - 12x + 20$
Factors of 20 that add to -12 are -10 and -2.
Answer: $(x - 10)(x - 2)$

11) $x^2 - 5x - 6$
Factors of -6 that add to -5 are -6 and 1.
Answer: $(x - 6)(x + 1)$

12) $x^2 - 1x - 90$
Factors of -90 that add to -1 are -10 and 9.
Answer: $(x - 10)(x + 9)$

13) $-7x^2 - 9x - 2$
Factor out negative: $-(7x^2 + 9x + 2)$.
Find factors of $7 \cdot 2 = 14$ that add to 9. They are 7 and 2.
Rewrite: $7x^2 + 7x + 2x + 2$.
Group: $7x(x + 1) + 2(x + 1)$.
Inside becomes $(7x + 2)(x + 1)$. Add the negative back.
Answer: $-(7x + 2)(x + 1)$

14) $x^2 - 2x - 35$
Factors of -35 that add to -2 are -7 and 5.
Answer: $(x - 7)(x + 5)$

15) $x^2 + 1x - 30$
Factors of -30 that add to 1 are 6 and -5.
Answer: $(x + 6)(x - 5)$

16) $x^2 - 2x - 99$
Factors of -99 that add to -2 are -11 and 9.
Answer: $(x - 11)(x + 9)$

17) $x^2 + 16x + 63$
Factors of 63 that add to 16 are 9 and 7.
Answer: $(x + 9)(x + 7)$

18) $x^2 - 18x + 80$
Factors of 80 that add to -18 are -10 and -8.
Answer: $(x - 10)(x - 8)$

19) $x^2 + 15x + 56$
Factors of 56 that add to 15 are 8 and 7.
Answer: $(x + 8)(x + 7)$

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

21) $x^2 + 17x + 72$
Factors of 72 that add to 17 are 9 and 8.
Answer: $(x + 9)(x + 8)$

22) $x^2 + 19x + 88$
Factors of 88 that add to 19 are 11 and 8.
Answer: $(x + 11)(x + 8)$

23) $x^2 + 3x - 4$
Factors of -4 that add to 3 are 4 and -1.
Answer: $(x + 4)(x - 1)$

24) $x^2 - 1x - 30$
Factors of -30 that add to -1 are -6 and 5.
Answer: $(x - 6)(x + 5)$

25) $x^2 + 16x + 63$
(Same as #17) Factors of 63 that add to 16 are 9 and 7.
Answer: $(x + 9)(x + 7)$

26) $x^2 + 9x + 14$
(Same as #8) Factors of 14 that add to 9 are 7 and 2.
Answer: $(x + 7)(x + 2)$

27) $15x^2 + 10x - 5$
First, factor out the greatest common factor, which is 5: $5(3x^2 + 2x - 1)$.
Now factor the inside part. We need factors of $3 \cdot -1 = -3$ that add to 2. They are 3 and -1.
Rewrite: $3x^2 + 3x - 1x - 1$.
Group: $3x(x + 1) - 1(x + 1)$.
Inside becomes $(3x - 1)(x + 1)$. Multiply by the 5 we pulled out.
Answer: $5(3x - 1)(x + 1)$

28) $-12x^2 - 26x - 12$
First, factor out the greatest common factor, which is -2: $-2(6x^2 + 13x + 6)$.
Now factor the inside. We need factors of $6 \cdot 6 = 36$ that add to 13. They are 9 and 4.
Rewrite: $6x^2 + 9x + 4x + 6$.
Group: $3x(2x + 3) + 2(2x + 3)$.
Inside becomes $(3x + 2)(2x + 3)$. Multiply by the -2.
Answer: $-2(3x + 2)(2x + 3)$

29) $x^2 + 7x + 10$
Factors of 10 that add to 7 are 5 and 2.
Answer: $(x + 5)(x + 2)$

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

Final Answer:
1) $(x + 9)(x + 2)$
2) $(x + 11)(x - 9)$
3) $(x - 7)(x + 5)$
4) $-(2x + 9)(x + 1)$
5) $(x - 5)(x + 4)$
6) $(x - 8)(x + 8)$
7) $(x - 4)(x - 2)$
8) $(x + 7)(x + 2)$
9) $(4x + 7)(x - 1)$
10) $(x - 10)(x - 2)$
11) $(x - 6)(x + 1)$
12) $(x - 10)(x + 9)$
13) $-(7x + 2)(x + 1)$
14) $(x - 7)(x + 5)$
15) $(x + 6)(x - 5)$
16) $(x - 11)(x + 9)$
17) $(x + 9)(x + 7)$
18) $(x - 10)(x - 8)$
19) $(x + 8)(x + 7)$
20) $(x - 7)(x - 1)$
21) $(x + 9)(x + 8)$
22) $(x + 11)(x + 8)$
23) $(x + 4)(x - 1)$
24) $(x - 6)(x + 5)$
25) $(x + 9)(x + 7)$
26) $(x + 7)(x + 2)$
27) $5(3x - 1)(x + 1)$
28) $-2(3x + 2)(2x + 3)$
29) $(x + 5)(x + 2)$
30) $(x + 7)(x + 4)$