Math CentralQuandaries & Queries


Question from victoria, a student:

hi my names victoria and i have been stuck on this question for ages can you please help me!
(x+2) is a factor of x^3+bx^2-14x+24. Find the value of b?

Hi Victoria,

What you want to use is that fact that if f(x) is a polynomial and (x - a) is a factor of the polynomial than f(a) = 0. This is easy to see because if (x - a) is a factor of f(x) then

f(x) = (x - a) g(x)

where g(x) is some polynomial. Now substitute x = a and the left side is f(a) and the right side is (a - a) g(a) = 0.

In your problem f(x) = x3+bx2-14x+24 and a = -2. Thus f(-2) = 0. So evaluate f(-2) and the resulting equation f(-2) = 0 you can solve for b.


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