SOLUTION: Given P(x)={{{(x^4-7x^2+4x+20)}}} show that(x+2)is a factor forP(x). How do you know?

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Question 165310: Given P(x)=%28x%5E4-7x%5E2%2B4x%2B20%29 show that(x+2)is a factor forP(x). How do you know?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You can apply the "Remainder/Factor theorem" which basically states that:
"If the function P(x) is divided by (x+a) and the remainder is zero, then (x+a) is a factor of P(x).
When you do this division, (%28x%5E4-7x%5E2%2B4x%2B20%29%2F%28x%2B2%29) you will find that you get x%5E3-2x%5E2-3x%2B10 with a zero remainder. So (x+2) must be a factor of the given function (P(x)).