Question

for the given polynomial p(x) and the given c, use the remainder theorem to find p(c). p(x)=3x^3 - 6x^2 - 5x + 7; - 2 p(c)= (simplify your answer.)

Explanation:

Step1: Substitute $c = - 2$ into $P(x)$

$P(-2)=3(-2)^{3}-6(-2)^{2}-5(-2)+7$

Step2: Calculate each term

$(-2)^{3}=-8$, so $3(-2)^{3}=3\times(-8)= - 24$; $(-2)^{2}=4$, so $6(-2)^{2}=6\times4 = 24$; $-5(-2)=10$.
$P(-2)=-24 - 24+10 + 7$

Step3: Simplify the expression

$P(-2)=(-24-24)+(10 + 7)=-48 + 17=-31$

Answer:

$-31$