Grade 9 Factoring Trinomials Worksheets 2024 - Free Printable

Problem: Factor the following trinomials completely. Look for a GCF first.

We will solve each problem step by step, factoring the trinomials as required. Let's go through them one by one.

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#### 1. \( x^2 + 13x - 30 \)

To factor \( x^2 + 13x - 30 \):
- We need two numbers that multiply to \(-30\) (the constant term) and add up to \(13\) (the coefficient of \(x\)).
- The numbers are \(15\) and \(-2\) because \(15 \times (-2) = -30\) and \(15 + (-2) = 13\).

Thus, we can write:
\[
x^2 + 13x - 30 = (x + 15)(x - 2)
\]

#### 2. \( x^2 - 5x - 24 \)

To factor \( x^2 - 5x - 24 \):
- We need two numbers that multiply to \(-24\) and add up to \(-5\).
- The numbers are \(-8\) and \(3\) because \((-8) \times 3 = -24\) and \((-8) + 3 = -5\).

Thus, we can write:
\[
x^2 - 5x - 24 = (x - 8)(x + 3)
\]

#### 3. \( x^2 + 5x - 36 \)

To factor \( x^2 + 5x - 36 \):
- We need two numbers that multiply to \(-36\) and add up to \(5\).
- The numbers are \(9\) and \(-4\) because \(9 \times (-4) = -36\) and \(9 + (-4) = 5\).

Thus, we can write:
\[
x^2 + 5x - 36 = (x + 9)(x - 4)
\]

#### 4. \( x^2 + 15x + 56 \)

To factor \( x^2 + 15x + 56 \):
- We need two numbers that multiply to \(56\) and add up to \(15\).
- The numbers are \(7\) and \(8\) because \(7 \times 8 = 56\) and \(7 + 8 = 15\).

Thus, we can write:
\[
x^2 + 15x + 56 = (x + 7)(x + 8)
\]

#### 5. \( x^2 + 15x + 54 \)

To factor \( x^2 + 15x + 54 \):
- We need two numbers that multiply to \(54\) and add up to \(15\).
- The numbers are \(6\) and \(9\) because \(6 \times 9 = 54\) and \(6 + 9 = 15\).

Thus, we can write:
\[
x^2 + 15x + 54 = (x + 6)(x + 9)
\]

#### 6. \( x^2 - 8x - 20 \)

To factor \( x^2 - 8x - 20 \):
- We need two numbers that multiply to \(-20\) and add up to \(-8\).
- The numbers are \(-10\) and \(2\) because \((-10) \times 2 = -20\) and \((-10) + 2 = -8\).

Thus, we can write:
\[
x^2 - 8x - 20 = (x - 10)(x + 2)
\]

#### 7. \( x^2 + 4x - 32 \)

To factor \( x^2 + 4x - 32 \):
- We need two numbers that multiply to \(-32\) and add up to \(4\).
- The numbers are \(8\) and \(-4\) because \(8 \times (-4) = -32\) and \(8 + (-4) = 4\).

Thus, we can write:
\[
x^2 + 4x - 32 = (x + 8)(x - 4)
\]

#### 8. \( x^2 - x - 20 \)

To factor \( x^2 - x - 20 \):
- We need two numbers that multiply to \(-20\) and add up to \(-1\).
- The numbers are \(-5\) and \(4\) because \((-5) \times 4 = -20\) and \((-5) + 4 = -1\).

Thus, we can write:
\[
x^2 - x - 20 = (x - 5)(x + 4)
\]

#### 9. \( x^2 + 11x + 30 \)

To factor \( x^2 + 11x + 30 \):
- We need two numbers that multiply to \(30\) and add up to \(11\).
- The numbers are \(5\) and \(6\) because \(5 \times 6 = 30\) and \(5 + 6 = 11\).

Thus, we can write:
\[
x^2 + 11x + 30 = (x + 5)(x + 6)
\]

#### 10. \( x^2 + 14x + 49 \)

To factor \( x^2 + 14x + 49 \):
- Notice that this is a perfect square trinomial: \( x^2 + 14x + 49 = (x + 7)^2 \).

Thus, we can write:
\[
x^2 + 14x + 49 = (x + 7)^2
\]

#### 11. \( x^2 + 10x + 16 \)

To factor \( x^2 + 10x + 16 \):
- We need two numbers that multiply to \(16\) and add up to \(10\).
- The numbers are \(2\) and \(8\) because \(2 \times 8 = 16\) and \(2 + 8 = 10\).

Thus, we can write:
\[
x^2 + 10x + 16 = (x + 2)(x + 8)
\]

#### 12. \( x^2 + 3x + 2 \)

To factor \( x^2 + 3x + 2 \):
- We need two numbers that multiply to \(2\) and add up to \(3\).
- The numbers are \(1\) and \(2\) because \(1 \times 2 = 2\) and \(1 + 2 = 3\).

Thus, we can write:
\[
x^2 + 3x + 2 = (x + 1)(x + 2)
\]

#### 13. \( x^2 + 15x + 44 \)

To factor \( x^2 + 15x + 44 \):
- We need two numbers that multiply to \(44\) and add up to \(15\).
- The numbers are \(4\) and \(11\) because \(4 \times 11 = 44\) and \(4 + 11 = 15\).

Thus, we can write:
\[
x^2 + 15x + 44 = (x + 4)(x + 11)
\]

#### 15. \( x^2 + 6x + 5 \)

To factor \( x^2 + 6x + 5 \):
- We need two numbers that multiply to \(5\) and add up to \(6\).
- The numbers are \(1\) and \(5\) because \(1 \times 5 = 5\) and \(1 + 5 = 6\).

Thus, we can write:
\[
x^2 + 6x + 5 = (x + 1)(x + 5)
\]

#### 16. \( 2x^2 + 20x + 32 \)

First, factor out the greatest common factor (GCF), which is \(2\):
\[
2x^2 + 20x + 32 = 2(x^2 + 10x + 16)
\]

Now, factor \( x^2 + 10x + 16 \):
- We need two numbers that multiply to \(16\) and add up to \(10\).
- The numbers are \(2\) and \(8\) because \(2 \times 8 = 16\) and \(2 + 8 = 10\).

Thus, we can write:
\[
x^2 + 10x + 16 = (x + 2)(x + 8)
\]

So, the complete factorization is:
\[
2x^2 + 20x + 32 = 2(x + 2)(x + 8)
\]

#### 18. \( 3x^2 - 15x + 18 \)

First, factor out the greatest common factor (GCF), which is \(3\):
\[
3x^2 - 15x + 18 = 3(x^2 - 5x + 6)
\]

Now, factor \( x^2 - 5x + 6 \):
- We need two numbers that multiply to \(6\) and add up to \(-5\).
- The numbers are \(-2\) and \(-3\) because \((-2) \times (-3) = 6\) and \((-2) + (-3) = -5\).

Thus, we can write:
\[
x^2 - 5x + 6 = (x - 2)(x - 3)
\]

So, the complete factorization is:
\[
3x^2 - 15x + 18 = 3(x - 2)(x - 3)
\]

#### 19. \( 2x^2 + 8x - 24 \)

First, factor out the greatest common factor (GCF), which is \(2\):
\[
2x^2 + 8x - 24 = 2(x^2 + 4x - 12)
\]

Now, factor \( x^2 + 4x - 12 \):
- We need two numbers that multiply to \(-12\) and add up to \(4\).
- The numbers are \(6\) and \(-2\) because \(6 \times (-2) = -12\) and \(6 + (-2) = 4\).

Thus, we can write:
\[
x^2 + 4x - 12 = (x + 6)(x - 2)
\]

So, the complete factorization is:
\[
2x^2 + 8x - 24 = 2(x + 6)(x - 2)
\]

#### 20. \( 2x^2 + 16x - 32 \)

First, factor out the greatest common factor (GCF), which is \(2\):
\[
2x^2 + 16x - 32 = 2(x^2 + 8x - 16)
\]

Now, factor \( x^2 + 8x - 16 \):
- We need two numbers that multiply to \(-16\) and add up to \(8\).
- The numbers are \(8\) and \(-2\) because \(8 \times (-2) = -16\) and \(8 + (-2) = 8\).

Thus, we can write:
\[
x^2 + 8x - 16 = (x + 8)(x - 2)
\]

So, the complete factorization is:
\[
2x^2 + 16x - 32 = 2(x + 8)(x - 2)
\]

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Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ (x + 15)(x - 2) \\
2. & \ (x - 8)(x + 3) \\
3. & \ (x + 9)(x - 4) \\
4. & \ (x + 7)(x + 8) \\
5. & \ (x + 6)(x + 9) \\
6. & \ (x - 10)(x + 2) \\
7. & \ (x + 8)(x - 4) \\
8. & \ (x - 5)(x + 4) \\
9. & \ (x + 5)(x + 6) \\
10. & \ (x + 7)^2 \\
11. & \ (x + 2)(x + 8) \\
12. & \ (x + 1)(x + 2) \\
13. & \ (x + 4)(x + 11) \\
15. & \ (x + 1)(x + 5) \\
16. & \ 2(x + 2)(x + 8) \\
18. & \ 3(x - 2)(x - 3) \\
19. & \ 2(x + 6)(x - 2) \\
20. & \ 2(x + 8)(x - 2)
\end{aligned}
}
\]