What is the remainder theorem and how do I apply it?
I understand that when a polynomial p(x) is divided by (x-a), the remainder is p(a). But I am not sure how to use this to check if (x-2) is a factor of x^3 - 3x + 2.
1 Answer
NRNikhil Rao
✓ Accepted
· 14d ago
▲ 13
To check if (x-2) is a factor of p(x) = x^3 - 3x + 2, substitute x = 2: p(2) = 8 - 6 + 2 = 4. Since p(2) = 4, not 0, (x-2) is NOT a factor. The factor theorem states (x-a) is a factor if and only if p(a) = 0. Try x = 1: p(1) = 1 - 3 + 2 = 0. So (x-1) IS a factor. You can then divide to find the other factors.
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