Use the Factor Theorem to determine whether x - c is a factor of f(x).
-$$( x ) = x ^ { 3 } + 4 x ^ { 2 } - 10 x + 12 ; x + 6$$
A)Yes
B)No

Question

Quizplus · Accepted Answer

The Factor Theorem states that $x - c$ is a factor of $f(x)$ if and only if $f(c) = 0$. Here, $c = -6$. Substituting $x = -6$ into $f(x)$, we get $f(-6) = (-6)^3 + 4(-6)^2 - 10(-6) + 12 = -216 + 144 + 60 + 12 = 0$. Since $f(-6) = 0$, $x + 6$ is a factor of $f(x)$.

Use the Factor Theorem to Determine Whether X - C (x)=x3+4x2−10x+12;x+6( x ) = x ^ { 3 } + 4 x ^ { 2 } - 10 x + 12 ; x + 6(x)=x3+4x2−10x+12;x+6

Use the Factor Theorem to Determine Whether X - C $( x ) = x ^ { 3 } + 4 x ^ { 2 } - 10 x + 12 ; x + 6$