Q. 451

Factor completely:

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

Verified

Answer

The factored polynomial is,

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

1Step 1. Given the information.

The polynomial function is,

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

2Step 2. Factoring the polynomial.

$9 s^{2} - 12 s + 4$

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

$= 9 s^{2} - 6 s - 6 s + 4 = (9 s^{2} - 6 s) - (6 s - 4)$

Taking out the common factors,

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

3Step 3. Checking the solution.

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

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

$= {(3 s)}^{2} - 2 \times 3 s \times 2 + {(2)}^{2} = 9 s^{2} - 12 s + 4$

This is true.