Question

factor the trinomial
$7y^4 + 11y^3 - 6y^2$
select the correct choice below and, if necessary, fill in the answer box to complete your choice
a. $7y^4 + 11y^3 - 6y^2 = \square$ (factor completely.)
b. $7y^4 + 11y^3 - 6y^2$ is prime.

Explanation:

Step1: Factor out GCF

Identify the greatest common factor (GCF) of all terms, which is $y^2$, and factor it out.
$7y^4 + 11y^3 - 6y^2 = y^2(7y^2 + 11y - 6)$

Step2: Factor quadratic trinomial

Factor the quadratic $7y^2 + 11y - 6$ by finding two numbers that multiply to $7\times(-6)=-42$ and add to 11 (these numbers are 14 and -3), then rewrite and factor.
$7y^2 + 11y - 6 = 7y^2 + 14y - 3y - 6 = 7y(y+2) - 3(y+2) = (7y-3)(y+2)$

Step3: Combine factors

Substitute the factored quadratic back into the expression from Step1.
$y^2(7y-3)(y+2)$

Answer:

A. $7y^4 + 11y^3 - 6y^2 = y^2(7y-3)(y+2)$ (Factor completely)