Part 1: Determine whether 2 is a zero of the polynomial P(x) = 3x3 – 6x2 – 3x – 18 by using the Remainder Theorem. Show your work. (4 points)

Part 2: Explain how the Remainder Theorem is useful in finding the zeros of a polynomial function. (4 points)

Question

Part 1: Determine whether 2 is a zero of the polynomial P(x) = 3x3 – 6x2 – 3x – 18 by using the Remainder Theorem. Show your work. (4 points)

Part 2: Explain how the Remainder Theorem is useful in finding the zeros of a polynomial function. (4 points)

hero · Answer

If 2 is a zero of the polynomial, then P(2) = 0

hero · Answer

P(x) = 3x^3 - 6x^2 - 3x - 18
P(2) = 3(2)^3 - 6(2)^2 - 3(2) - 18
P(2) = 3(8) - 6(4) - 6 - 18
P(2) = 24 - 24 - 6 - 18
P(2) = 0 - 6 - 18
P(2) = -24

However, since P(2) = -24, 2 is not a zero of the polynomial function P(x).