Question

Determine whether 9x^2 – 120x – 400 is a perfect square trinomial. If so, choose the correct factorization.

Answer 1

Given the expression

$9x^2-120x-400$

9 is a perfect square of

$9=(3)^2$

400 is also a perfect square of

$400=(20)^2$

Both the x-term and the constant are negative, which indicates that this polynomial is the result of a difference of squares:

$(a+b)(a-b)=a^2-ab+ab-b^2=a^2-b^2$

So the original factorization is

$(3x+20)(3x-20)$