Question

Factor completely:

$9s^2-12s+4$.

Short answer

The factored polynomial is,

${(3s-2)}^2$.

Step-by-step solution

Step 1. Given the information.

The polynomial function is,

$9s^2-12x+4$.

Step 2. Factoring the polynomial.

$9s^2-12s+4$

Splitting the middle term such that the sum of the terms is $(-12)$and the product of the terms is $36$.

$$\begin{gathered} =9s^2-6s-6s+4 \\ =(9s^2-6s)-(6s-4) \end{gathered}$$

Taking out the common factors,

$$\begin{gathered} =3s(3s-2)-2(3s-2) \\ =(3s-2)(3s-2) \\ ={(3s-2)}^2 \end{gathered}$$

Step 3. Checking the solution.

${(3s-2)}^2$

Using the identity,${(a-b)}^2=a^2-2ab+b^2$,

role="math" localid="1644784547183" $$\begin{gathered} ={\left(3s\right)}^2-2\times 3s\times 2+{\left(2\right)}^2 \\ =9s^2-12s+4 \end{gathered}$$

This is true.