Let $P ( x ) = 3 x ^ { 3 } - 2 x ^ { 2 } + 4 x - 5$ . Evaluate $P ( - 2 )$ by substituting the given value of x into the polynomial and simplifying. Then evaluate the polynomial by using the remainder theorem and synthetic division.
A) -45
B) -44
C)44
D) -46
E) 47

Question

Quizplus · Accepted Answer

Substituting $x = -2$ into $P(x)$ gives $P(-2) = 3(-2)^3 - 2(-2)^2 + 4(-2) - 5 = -24 - 8 - 8 - 5 = -45$. The remainder theorem also yields -45 when dividing the polynomial by $x + 2$, confirming the result.

Let P(x)=3x3−2x2+4x−5P ( x ) = 3 x ^ { 3 } - 2 x ^ { 2 } + 4 x - 5P(x)=3x3−2x2+4x−5

Let $P ( x ) = 3 x ^ { 3 } - 2 x ^ { 2 } + 4 x - 5$