Factoring Trinomials Worksheet | PDF Printable Algebra Worksheet - Free Printable

Here are the factored forms for all the quadratic expressions in the worksheet.

Section A

*(These trinomials start with $x^2$. We look for two numbers that multiply to the last number and add up to the middle number.)*

1) $(x + 10)(x - 3)$
2) $(x + 4)(x + 5)$
3) $(x + 9)(x - 1)$
4) $(x - 8)(x - 10)$
5) $(x - 4)(x - 7)$
6) $(x + 12)(x - 6)$
7) $(x - 11)(x + 2)$
8) $(x - 4)(x + 3)$
9) $(x + 12)(x - 9)$
10) $(x - 8)(x - 9)$
11) $(x - 7)(x + 6)$
12) $(x - 7)(x - 8)$

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Section B

*(These have a $2$ in front of the $x^2$. We use grouping or trial and error to find factors like $(2x + \dots)(x + \dots)$.)*

1) $(2x + 1)(x + 1)$
2) $(2x + 1)(x + 2)$
3) $(2x + 1)(x + 3)$
4) $(2x + 5)(x + 1)$
5) $(2x + 7)(x + 1)$
6) $(2x + 3)(x + 1)$
7) $2(x + 1)(x + 3)$ *(Factor out 2 first: $2(x^2+4x+3)$)*
8) $(2x + 5)(x + 2)$
9) $2(x + 1)(x + 7)$ *(Factor out 2 first: $2(x^2+8x+7)$)*
10) $2(x + 2)(x + 6)$ *(Factor out 2 first: $2(x^2+8x+12)$)*
11) $2(x + 3)(x + 3)$ *(Factor out 2 first: $2(x^2+6x+9)$)*
12) $2(x + 2)(x + 5)$ *(Factor out 2 first: $2(x^2+7x+10)$)*
13) $2(x + 2)(x + 9)$ *(Factor out 2 first: $2(x^2+11x+18)$)*
14) $2(x + 4)(x + 6)$ *(Factor out 2 first: $2(x^2+14x+24)$)*
15) $2(x + 4)(x + 9)$ *(Factor out 2 first: $2(x^2+13x+36)$)*

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Section C

*(These involve negative signs. Be careful with your plus and minus symbols.)*

1) $(2x - 1)(x + 1)$
2) $(2x - 3)(x + 1)$
3) $(2x - 1)(x + 5)$
4) $(2x + 1)(x - 2)$
5) $(2x + 3)(x - 8)$
6) $(3x + 1)(x - 5)$
7) $(3x + 1)(x - 3)$ *Wait, let me double check #7.*
*Check:* $(3x+1)(x-3) = 3x^2 -9x + x -3 = 3x^2 -8x -3$. The problem is $3x^2 -8x -11$.
*Correction for #7:* Factors of $3 \times -11 = -33$ that add to $-8$ are $-11$ and $3$.
Split middle term: $3x^2 -11x + 3x -11$. Group: $x(3x-11) + 1(3x-11)$.
Result: $(x + 1)(3x - 11)$.
8) $2(x - 3)(x - 2)$ *(Factor out 2 first: $2(x^2 - 7x + 6)$)*
9) $3(x - 3)(x - 4)$ *(Factor out 3 first: $3(x^2 - 7x + 12)$)*
10) $(5x - 1)(x - 8)$
11) $(3x + 7)(x - 3)$
12) $2(x + 3)(x - 2)$ *(Factor out 2 first: $2(x^2 + x - 6)$)*
13) $(2x - 5)(x - 3)$
14) $(3x + 2)(x - 12)$
15) $(5x - 2)(x - 5)$

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Section D

*(These are harder because the first number is larger than 2, or there are common factors to pull out first.)*

1) $4(x + 1)(x + 2)$ *(Factor out 4 first: $4(x^2 + 3x + 2)$)*
2) $(2x + 5)(3x + 4)$
3) $6(x + 1)(x + 3)$ *(Factor out 6 first: $6(x^2 + 4x + 3)$)*
4) $(4x + 7)(x + 3)$
5) $2(2x + 9)(x + 1)$ *(Factor out 2 first: $2(2x^2 + 11x + 9)$)*
6) $(4x + 3)(2x + 5)$
7) $4(2x + 1)(x + 4)$ *(Factor out 4 first: $4(2x^2 + 9x + 4)$)*
8) $(3x - 4)(2x + 1)$
9) $(2x - 3)(3x - 5)$
10) $8(x + 3)(x - 1)$ *(Factor out 8 first: $8(x^2 + 2x - 3)$)*
11) $(7x - 4)(x + 8)$
12) $(2x - 7)(3x - 8)$
13) $(3x + 5)(3x + 7)$
14) $6(2x - 5)(x - 1)$ *(Factor out 6 first: $6(2x^2 - 7x + 5)$)*
15) $24(2x + 1)(x + 1)$ *(Factor out 24 first: $24(2x^2 + 3x + 1)$)*
16) $(2x + 1)(9x + 8)$
17) $(4x + 3)(5x + 3)$
18) $2(3x - 4)(5x - 1)$ *(Factor out 2 first: $2(15x^2 - 16x + 4)$)*
19) $4(3x - 1)(3x + 2)$ *(Factor out 4 first: $4(9x^2 + 10.5x - 2)$... wait, simpler to factor GCF 2? No, GCF is 2. Let's recheck 19. $36x^2+42x-8$. GCF is 2. $2(18x^2+21x-4)$. Factors of $18*-4=-72$ adding to 21 are 24 and -3. $2(18x^2+24x-3x-4) \rightarrow 2[6x(3x+4)-1(3x+4)] \rightarrow 2(6x-1)(3x+4)$.)*
*Correction for 19:* $2(6x - 1)(3x + 4)$
20) $2(4x + 1)(3x - 7)$ *(Factor out 2 first: $2(12x^2 - 25x - 7)$)*
21) $-(2x + 7)(x - 3)$ or $(7 - 2x)(x + 3)$