Question

factor.
$4y^{2}+16y - 9$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(4\times(-9)= -36\) and add up to \(16\). The numbers are \(18\) and \(-2\) since \(18\times(-2)= -36\) and \(18 + (-2)=16\).

Step2: Split the middle term

Rewrite the middle term \(16y\) as \(18y - 2y\):
\(4y^{2}+18y - 2y - 9\)

Step3: Group the terms

Group the first two terms and the last two terms:
\((4y^{2}+18y)+(-2y - 9)\)

Step4: Factor out the GCF from each group

Factor out \(2y\) from the first group and \(-1\) from the second group:
\(2y(2y + 9)-1(2y + 9)\)

Step5: Factor out the common binomial

Factor out \((2y + 9)\):
\((2y + 9)(2y - 1)\)

Answer:

\((2y + 9)(2y - 1)\)