How can I show that (x+2) is a factor of without doing long division? |
You are right - there is a 'short cut' method:
If a is a root of a polynomial, then (x - a) is a factor of that polynomial |
All you have to do, to show that (x + 2) is a factor of f(x), is to evaluate f(-2).
In other words, work out f(x) with x = -2:
f(-2) = (-2)^{4} + 2×(-2)^{3} - 7×(-2)^{2} - 8×(-2) + 12 f(-2) = 16 - 16 - 28 + 16 + 12 f(-2) = 0 |
Because f(-2) = 0, (x + 2) is a factor of f(x). |