Question

Which binomial is NOT a factor of the expression x 3 – 11x 2 + 16x + 84? [1] x-5 [2] 2x-6 [3] x+7

Answer 1

Answer:

It's much easier to check if a given polynomial is a factor than it is to entirely factor it.

For example, you can always do polynomial long division and check if the remainder is zero. For the special case of linear factors x - a, you can do synthetic division (before anyone says anything, yes, I know that there's a form of synthetic division for higher degree divisors, but it's not commonly taught).

Another approach is the rational root theorem. For ax + b to be a factor of a polynomial, with a and b both integers, it's necessary (but not sufficient) for a to be a factor of the leading term of the polynomial and for b to be a factor of the constant term. So that would rule out a factor like 2x - 9, since 9 isn't a factor of 84.