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

Answer:

Option A. (9x - 12)²

Step-by-step 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

Answer:

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

Step-by-step 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.