Question

question 6 of 10
which of the following is the correct factorization of the polynomial below?
2x² - 8x + 8

a. 2(x + 2)(x + 4)

b. (2x + 4)(x + 4)

c. 2(x - 2)²

d. the polynomial is irreducible.

Explanation:

Step1: Factor out the GCF

The polynomial is \(2x^2 - 8x + 8\). The greatest common factor (GCF) of the terms is 2. Factor out 2: \(2(x^2 - 4x + 4)\).

Step2: Factor the quadratic

The quadratic \(x^2 - 4x + 4\) is a perfect square trinomial. It factors as \((x - 2)^2\) because \((x - 2)^2 = x^2 - 4x + 4\).

Step3: Combine the factors

Putting it together, the factored form is \(2(x - 2)^2\).

Answer:

C. \(2(x - 2)^2\)