Question

which expression is the result of factoring the expression below by taking out its greatest common factor?\\(6x^2 - 3x + 12 =?\\)\
choose 1 answer:\
a \\(6(x^2 - 3x + 2)\\)

Explanation:

Step1: Identify GCF of coefficients

The coefficients are 6, -3, 12. Their GCF is 3.

Step2: Factor out GCF from each term

Divide each term by 3:
$6x^2 \div 3 = 2x^2$, $-3x \div 3 = -x$, $12 \div 3 = 4$
Write as factored form: $3(2x^2 - x + 4)$

Step3: Verify given option A

Expand option A: $6(x^2 - 3x + 2) = 6x^2 - 18x + 12$, which does not match the original expression.

Answer:

The correct factored form (not fully shown in the provided options) is $3(2x^2 - x + 4)$; option A is incorrect as it does not match the original expression when expanded.