Question

Factor completely:

$4p^2-16p+12$

Short answer

The factored form is $4(p-3)(p-1)$.

Step-by-step solution

Step 1. Given Information 

We are given a polynomial $4p^2-16p+12$,

We have to factor the given polynomial.

Step 2. Factoring the polynomial   

Factoring out GCF $4$, we get

$4p^2-16p+12=4\left(p^2-4p+3\right)$

Using middle terms splitting or acmethod, we get

$4p^2-16p+12=4\left(p^2-3p-p+3\right)$

Grouping the terms, we get

role="math" localid="1647833420742" $$\begin{gathered} 4p^2-16p+12=4\left(\left(p^2-3p\right)+(-p+3)\right) \\ 4p^2-16p+12=4\left(p\right(p-3)-1(p-3\left)\right) \end{gathered}$$

Factoring out GCF$p-3$, we get

$4p^2-16p+12=4(p-3)(p-1)$

Step 3. Checking the factors   

Multiplying the factors, we get

$$\begin{gathered} 4(p-3)(p-1)=4p^2-16p+12 \\ 4\left(p\right(p-3)-1(p-3\left)\right)=4p^2-16p+12 \\ 4\left(p^2-3p-p+3\right)=4p^2-16p+12 \\ 4\left(p^2-4p+3\right)=4p^2-16p+12 \\ 4p^2-16p+12=4p^2-16p+12 \\ LHS=RHS \end{gathered}$$

Hence, the factors are correct.