Question

which binomial is a factor of 9x2 – 64? 3x – 8 9x – 32 3x 32 9x 8

Answer 1

That would be 3x - 8.

(3x - 8) x (3x + 8)

Answer 2

Consider binomial $9x^2 - 64.$

You know that

$9=3^2,\\ 64=8^2$

and

$a^2\cdot b^2=(ab)^2.$

Then

$9x^2 - 64=3^2\cdot x^2-8^2=(3x)^2-8^2.$

Use formula $a^2-b^2=(a-b)(a+b),$

thus

$9x^2 - 64=(3x)^2-8^2=(3x-8)(3x+8).$

Answer: correct choice is A, 3x-8.