Question

factor completely 8h²+36h+16; options: 4(2h+1)(h+4); 2(4h+1)(h+2); 4h(2+h)(h+1); h(8+1)(2+h)

Explanation:

Step1: Factor out GCF

$$\begin{align*} 8h^2+36h+16 &= 4(2h^2+9h+4) \end{align*}$$

Step2: Factor quadratic trinomial

Find two numbers that multiply to $2\times4=8$ and add to $9$: $8$ and $1$. Split the middle term:

$$\begin{align*} 2h^2+9h+4 &= 2h^2+8h+h+4 \\ &= 2h(h+4)+1(h+4) \\ &= (2h+1)(h+4) \end{align*}$$

Step3: Combine factors

Substitute back into the expression from Step1:
$4(2h+1)(h+4)$

Answer:

4(2h+1) (h+4)