Use the remainder theorem and synthetic division to find $P ( - 2 )$ for $P ( x ) = 3 x ^ { 3 } + 4 x - 5$ .
A) -37
B) 27
C) 15
D) 17

Question

Quizplus · Accepted Answer

To find $P(-2)$ using synthetic division, we set up the division with -2 as the divisor and the coefficients of $P(x)$ as the dividend. The polynomial $P(x) = 3x^3 + 0x^2 + 4x - 5$ (note the inclusion of $0x^2$ for the missing $x^2$ term). Synthetic division proceeds as follows:1. Bring down the leading coefficient (3).2. Multiply -2 (the root) by the value just written (3), getting -6, and write this under the next coefficient (0).3. Add the values in the second column (0 + -6 = -6), and write this result down.4. Repeat the multiply-add process: Multiply -2 by -6 (getting 12), add this to 4 (getting 16), and write it down.5. Finally, multiply -2 by 16 (getting -32), and add this to -5, yielding -37.Thus, the remainder, which is also $P(-2)$, is -37.

Use the Remainder Theorem and Synthetic Division to Find P(−2)P ( - 2 )P(−2)

Use the Remainder Theorem and Synthetic Division to Find $P ( - 2 )$