Question

14 factor by gcf
$9y^{3}+12y^{2}-6y+27$
$3y(3y^{2}+4y+9)$
$3(3y^{3}+4y^{2}-2y-9)$
$9(y^{3}+2y^{2}-y+3)$
$3(3y^{3}+4y^{2}-2y+9)$

Explanation:

Step1: Find GCF of coefficients

Coefficients: 9, 12, -6, 27. GCF = 3.

Step2: Factor out GCF from each term

$9y^3 = 3 \times 3y^3$, $12y^2 = 3 \times 4y^2$, $-6y = 3 \times (-2y)$, $27 = 3 \times 9$

Step3: Rewrite expression with GCF factored

$3(3y^3 + 4y^2 - 2y + 9)$

Answer:

$3(3y^3+4y^2-2y+9)$ (the bottom-right option)