Questions: Use the Remainder Theorem to evaluate the polynomial function. P(z)=2z^3-4z^2+3z-3 ; P(-2) P(-2)=

Transcript text: Use the Remainder Theorem to evaluate the polynomial function. \[ \begin{array}{l} \quad P(z)=2 z^{3}-4 z^{2}+3 z-3 ; P(-2) \\ P(-2)= \end{array} \] Need Help? Read It Submit Answer

Solution

Solution Steps

To evaluate the polynomial function \( P(z) = 2z^3 - 4z^2 + 3z - 3 \) at \( z = -2 \) using the Remainder Theorem, substitute \( z = -2 \) into the polynomial and compute the result. The Remainder Theorem states that the remainder of the division of a polynomial \( P(z) \) by \( z - a \) is \( P(a) \).

Step 1: Evaluate the Polynomial

To evaluate the polynomial \( P(z) = 2z^3 - 4z^2 + 3z - 3 \) at \( z = -2 \), we substitute \( -2 \) into the polynomial:

\[ P(-2) = 2(-2)^3 - 4(-2)^2 + 3(-2) - 3 \]

Step 2: Calculate Each Term

Calculating each term separately: