Question

The difference between two trinomials is 5x2 + 11x − 16. If one of the trinomials is 3x2 − 2x + 7, then which expression could be the other trinomial?

Answer 1

We have

$p(x) - q(x) = 5x^2 + 11x - 16$

Also, suppose that $p(x) = 3x^2-2x+7$

So, we have

$3x^2-2x+7 - q(x) = 5x^2 + 11x - 16 \iff q(x) = 3x^2-2x+7 - (5x^2 + 11x - 16)=3x^2-2x+7 - 5x^2 - 11x + 16 = -2x^2-13x+23$