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.

Tags

CCSS.HSA-REI.B.4B

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).