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.

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

[tex]81x^2-216x+144[/tex]

[tex]=9(9x^2-24x+12)[/tex]

[tex]=9(9x^2-12x-12x+12)[/tex]

[tex]=9(3x(3x-4)-4(3x-4))[/tex]

[tex]=9(3x-4)(3x-4)[/tex]

[tex]=9(3x-4)^2[/tex]

[tex]=3^2(3x-4)^2[/tex]

[tex]=(3(3x-4))^2[/tex]

[tex]=(9x-12)^2[/tex]

Hence choice A. [tex]=(9x-12)^2[/tex] is correct.

eudora eudora · Answer 2 · 2019-06-15T19:34:12+02:00

eudora eudora

15-06-2019

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 Link