Factoring Polynomials Warmup

Suzie solves the equation below:
x² + 4x - 12 = 2
(x - 2)(x + 6) = 2, 
by setting x -2 = 0 and x + 6 = 0. 
Her solutions are x = 2 and x = -6.
Is Suzie correct? Why or why not?

• Yes, she factored correctly and then used the zero product property

• Yes, she factored correctly and then square rooted.

• No, she did factor correctly, but she can't use the zero product property as shown.

• No, she didn't factor correctly so the rest of her work is wrong. 

Answer explanation

No, she did factor correctly, but she can't use the zero product property as shown.

Factor:
24c⁵ - 12c³

• 6(4c⁵ - 2c³)

• 12c³(2c²)

• 12c³(2c² - 1)

• 12c³(2c² - 0)

Answer explanation

To factor out the greatest common factor, we take out 12c^3 from both terms: 12c^3(2c^2 - 1). Therefore, the correct choice is 12c^3(2c^2 - 1).

Factor:
18b²-9b³

• 9b²(18-9b)

• 9b²(2-b)

• 9b²(18-9b²)

• b²(2-b²)

Answer explanation

To factor out the common factor, 9b^2, from both terms, we get 9b^2(2-b). Therefore, the correct choice is 9b^2(2-b).

Find the factors of 5x²+20x+20

• 5(x+2)(x+2)

• 5(x-2)(x-2)

• 5(x+2)(x-2)

• (5x+2)(x+2)

Answer explanation

The correct factorization of 5x^2 + 20x + 20 is 5(x+2)(x+2) because the common factor of 5 is factored out first, then the quadratic expression is factored using the sum-product method.

Find the factors of 4x²-16x-9

• (2x-9)(2x+1)

• (2x+9)(2x-1)

• (4x-1)(x+9)

• (x+1)(4x-9)

Answer explanation

To factor 4x^2-16x-9, find two numbers that multiply to -36 (product of -9 and 4) and add up to -16. The numbers are -18 and 2. Therefore, the factors are (2x-9)(2x+1).

Factor:

x² + 2x – 3

• (x - 2)(x + 1)

• (x + 1)(x - 3)

• (x + 2)(x - 1)

• (x - 1)(x + 3)

Answer explanation

To factor x^2 + 2x - 3, find two numbers that multiply to -3 and add up to 2. The numbers are 3 and -1. Therefore, the factored form is (x - 1)(x + 3).

Factor:

x² + 9x - 36

• (x + 12)(x - 3)

• (x + 9)(x - 4)

• (x - 12)(x + 3)

• (x - 9)(x - 4)

Answer explanation

To factor x^2 + 9x - 36, find two numbers that multiply to -36 and add up to 9. The numbers are 12 and -3, so the factors are (x + 12)(x - 3).