Question

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

Answer 1

f(2)=2(2)^3-5(2)^2+4(2)=-2
2 is not a zero.
f(2) is the remainder you get when dividing P(x) by x-2. if the remainder is not 0, it is not a zero

Answer 2

sometimes it is more convenient to use synthetic division, especially with large numbers