Use the factor theorem and determine whether the first expression is a factor of P ( x ). $x + 2 ; P ( x ) = 4 x ^ { 2 } + 8 x + 3$ ( Hint : Write x+2 as $x - ( - 2 )$ .)
A) yes
B) no

Question

Quizplus · Accepted Answer

The factor theorem states that $x - c$ is a factor of $P(x)$ if and only if $P(c) = 0$. Here, $c = -2$. Substituting $-2$ into $P(x)$, we get $P(-2) = 4(-2)^2 + 8(-2) + 3 = 16 - 16 + 3 = 3$, which is not zero. Therefore, $x + 2$ is not a factor of $P(x)$.

Use the Factor Theorem and Determine Whether the First Expression x+2;P(x)=4x2+8x+3x + 2 ; P ( x ) = 4 x ^ { 2 } + 8 x + 3x+2;P(x)=4x2+8x+3

Use the Factor Theorem and Determine Whether the First Expression $x + 2 ; P ( x ) = 4 x ^ { 2 } + 8 x + 3$