Question

Which of the binomials below is a factor of this trinomial?

-3x2 - 21x + 24

Answer 1

Here's how to factor this:
\[-3x^2-21x+24\]\(-3\) is a common factor of all three terms:
\[-3*x^2-3(7x)-3(-8) = -3(x^2+7x-8)\]We'll set that \(-3\) aside until later, and concentrate on factoring the stuff in the parentheses:
\[x^2+7x-8\]We need to find two factors of \(-8\) that add to \(+7\).
\[-1*8\]\[-2*4\]\[-4*2\]\[-8*1\]Looks like \(-1,8\) is the clear choice.
\[x^2+7x-8 = (x-1)(x+8)\]and the complete factoring is\[-3(x-1)(x+8)\]

Checking our work:
\[-3(x-1)(x+8) = (-3x+3)(x+8) = -3x^2-24x+3x+24\]\[ = -3x^2-21x+24\checkmark\]