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| Math Central | Quandaries & Queries |
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Question from victoria, a student: hi my names victoria and i have been stuck on this question for ages can you please help me! |
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.
Penny
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