Question

wen is factoring the polynomial, which has four terms.
$6x^3 - 12x^2 + 7x - 14$
$6x^2(x - 2) + 7(x - 2)$
which is the completely factored form of his polynomial?
$(6x^2 + 7)(x - 2)$
$(6x^2 - 2)(x + 7)$
$(6x^2 - 7)(x + 2)$
$(6x^2 + 2)(x - 7)$

Explanation:

Step1: Identify common factor

The given intermediate form is $6x^2(x - 2) + 7(x - 2)$. Notice that $(x-2)$ is a common binomial factor.

Step2: Factor out the common binomial

Factor $(x-2)$ from both terms:
$(x - 2)(6x^2 + 7)$
This can also be written as $(6x^2 + 7)(x - 2)$ since multiplication is commutative.

Answer:

$(6x^2 + 7)(x - 2)$