Question

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

x2 + 19x + 84

A. x - 7
B. x2 + 12
C. x + 84
D. x + 7

Answer 1

\[x^2+19x+84\]The factors of that binomial are going to be\[(x+a)(x+b)\]where \(a*b = 84\) and \(a+b=19\)

We know this because if we multiply\[(x+a)(x+b) = x^2 + ax + bx + ab\]\[x^2+(a+b)x+ab\]and comparing that with our original equation\[x^2+19x+84\]it is clear that for everything to match, we must have\[(a+b)x=19x\]\[a+b=19\]and\[a*b=84\]

So, figure out the pairs of factors that multiply to 84. Choose the pair that sums to 19. Look in the answer table for one that contains the one of those two numbers.