50+ Factoring worksheets for 9th Grade on Quizizz | Free & Printable - Free Printable

Let's solve each of these factoring problems step by step.

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1. Which of the following is a factor of $ x^2 - 10x + 24 $?

We need to factor $ x^2 - 10x + 24 $.

We look for two numbers that:
- Multiply to 24 (the constant term)
- Add to -10 (the coefficient of the middle term)

Let’s list factor pairs of 24:
- $ 1 \times 24 $
- $ 2 \times 12 $
- $ 3 \times 8 $
- $ 4 \times 6 $

Now check which pair adds to -10:
- $ -4 + (-6) = -10 $, and $ (-4)(-6) = 24 $

So:
$$
x^2 - 10x + 24 = (x - 4)(x - 6)
$$

So the factors are $ x - 4 $ and $ x - 6 $.
Looking at the options:

A) $ x+6 $ → Not a factor
B) $ x-4 $ → ✔ Yes, this is a factor
C) $ x+4 $ → No
D) $ x-2 $ → No

✔ Answer: B) $ x - 4 $

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2. Factor: $ x^2 + 7x - 30 $

Find two numbers that:
- Multiply to -30
- Add to 7

Try pairs:
- $ 10 \times (-3) = -30 $, $ 10 + (-3) = 7 $ → ✔

So:
$$
x^2 + 7x - 30 = (x + 10)(x - 3)
$$

Check:
$$
(x + 10)(x - 3) = x^2 - 3x + 10x - 30 = x^2 + 7x - 30
$$

✔ Answer: D) $ (x + 10)(x - 3) $

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3. Factor: $ x^2 + 9x - 36 $

Find two numbers that:
- Multiply to -36
- Add to 9

Try:
- $ 12 \times (-3) = -36 $, $ 12 + (-3) = 9 $ → ✔

So:
$$
x^2 + 9x - 36 = (x + 12)(x - 3)
$$

Check:
$$
(x + 12)(x - 3) = x^2 - 3x + 12x - 36 = x^2 + 9x - 36
$$

✔ Answer: C) $ (x + 12)(x - 3) $

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4. Factor: $ a^2 - a - 12 $

Find two numbers that:
- Multiply to -12
- Add to -1

Try:
- $ -4 \times 3 = -12 $, $ -4 + 3 = -1 $ → ✔

So:
$$
a^2 - a - 12 = (a - 4)(a + 3)
$$

✔ Answer: A) $ (a - 4)(a + 3) $

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5. Which of the following is a factor of $ r^2 - 16r + 60 $?

Factor $ r^2 - 16r + 60 $

Find two numbers that:
- Multiply to 60
- Add to -16

Try:
- $ -10 \times -6 = 60 $, $ -10 + (-6) = -16 $ → ✔

So:
$$
r^2 - 16r + 60 = (r - 10)(r - 6)
$$

Factors are $ r - 10 $ and $ r - 6 $

Check options:
A) $ r + 10 $ → No
B) $ r - 6 $ → ✔ Yes
C) $ r - 30 $ → No
D) $ r + 6 $ → No

✔ Answer: B) $ r - 6 $

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6. Factor: $ x^2 - 16x + 48 $

Find two numbers that:
- Multiply to 48
- Add to -16

Try:
- $ -12 \times -4 = 48 $, $ -12 + (-4) = -16 $ → ✔

So:
$$
x^2 - 16x + 48 = (x - 12)(x - 4)
$$

Check:
$$
(x - 12)(x - 4) = x^2 - 4x - 12x + 48 = x^2 - 16x + 48
$$

✔ Answer: B) $ (x - 12)(x - 4) $

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✔ Final Answers:

1. B – $ x - 4 $
2. D – $ (x + 10)(x - 3) $
3. C – $ (x + 12)(x - 3) $
4. A – $ (a - 4)(a + 3) $
5. B – $ r - 6 $
6. B – $ (x - 12)(x - 4) $

Let me know if you'd like explanations for the rest!