Question

Determine whether 2 is a zero of the polynomial P(x) = 2x^3 – 5x^2 + 4x – 6 by using the Remainder Theorem. Explain how the Remainder Theorem is useful in finding the zeros of a polynomial function.

Answer 1

divide \(2x^3-5x^2+4x-6\) by \(x-2\) if the remainder is zero, then 2 is a zero of p(x) and you can factor p(x) as \(p(x)=(x-2)(\text{something})\)