Use the remainder theorem to find $\mathbf{P}(\mathbf{k})$.
-$\mathrm{k}=-3 ; \mathrm{P}(\mathrm{x})=-\mathrm{x}^{3}+2 \mathrm{x}^{2}-2$
A) 43
B) -6
C) -46
D) -43

Question

Quizplus · Accepted Answer

By the Remainder Theorem, when $P(x)$ is divided by $x-k$, the remainder is $P(k)$. So, to find $P(-3)$, we evaluate $P(x)$ at $x=-3$:$$P(-3) = -(-3)^3 + 2(-3)^2 - 2 = -(-27) + 2(9) - 2 = 27 + 18 - 2 = 43$$Therefore, $P(-3) = 43$.

Use the Remainder Theorem to Find P(k)\mathbf{P}(\mathbf{k})P(k) - k=−3;P(x)=−x3+2x2−2\mathrm{k}=-3 ; \mathrm{P}(\mathrm{x})=-\mathrm{x}^{3}+2 \mathrm{x}^{2}-2k=−3;P(x)=−x3+2x2−2

Use the Remainder Theorem to Find $\mathbf{P}(\mathbf{k})$
- $\mathrm{k}=-3 ; \mathrm{P}(\mathrm{x})=-\mathrm{x}^{3}+2 \mathrm{x}^{2}-2$