Question

which of the following is the correct factorization of the polynomial below? 2x^2 - 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 greatest - common factor

First, find the GCF of the coefficients 2, - 8, and 8. The GCF is 2. So, $2x^{2}-8x + 8=2(x^{2}-4x + 4)$.

Step2: Factor the quadratic expression

The quadratic expression $x^{2}-4x + 4$ is in the form of $a^{2}-2ab + b^{2}$ where $a = x$ and $b = 2$. Since $a^{2}-2ab + b^{2}=(a - b)^{2}$, then $x^{2}-4x + 4=(x - 2)^{2}$.
So, $2x^{2}-8x + 8=2(x - 2)^{2}$.

Answer:

C. $2(x - 2)^{2}$