Question

Determine whether the polynomial below can be factored into perfect squares. If so, factor the polynomial. Otherwise, select that it cannot be factored into a perfect square.

Answer 1

Option A. (9x - 12)²

Explanation:

We will factorize the given polynomial into perfect square.

The polynomial is 81x²- 216x + 144

We will take 9 common out of this polynomial first

81x² - 216x + 144 = 9(9x² - 24x + 16)

= 9[(3x)² - 2(3)(4)x + 4²]

= 9[(3x - 4)²

= 3²(3x - 4)²

= (9x - 12)²

Therefore, Option A. (9x - 12)² is the answer.

Answer 2

A.
`=(9x-12)^2`

Explanation:

We need to determine whether the polynomial
`81x^2-216x+144` can be factored into perfect squares. If so, factor the polynomial. Otherwise, select that it cannot be factored into a perfect square.

`81x^2-216x+144`

`=9(9x^2-24x+12)`

`=9(9x^2-12x-12x+12)`

`=9(3x(3x-4)-4(3x-4))`

`=9(3x-4)(3x-4)`

`=9(3x-4)^2`

`=3^2(3x-4)^2`

`=(3(3x-4))^2`

`=(9x-12)^2`

Hence choice A.
`=(9x-12)^2` is correct.