Use the Factor Theorem to determine whether x - c is a factor of f. If it is, write f in factored form, that is, write f in the
form f(x) = (x - c)(quotient).
-$$f ( x ) = 2 x ^ { 3 } + 16 x ^ { 2 } + 39 x + 45 ; c = - 5$$
A) $\mathrm { No }$
B) Yes; $f ( x ) = ( x - 5 ) \left( 2 x ^ { 2 } + 6 x - 9 \right)$
C) Yes; $f ( x ) = ( x + 5 ) \left( 2 x ^ { 2 } + x + 9 \right)$
D) Yes; $f ( x ) = ( x + 5 ) \left( 2 x ^ { 2 } + 6 x + 9 \right)$

Question

Quizplus · Accepted Answer

To determine if $x - c$ is a factor of $f(x)$, substitute $c$ into $f(x)$. Here, $c = -5$, so we check if $f(-5) = 0$. Substituting $-5$ into $f(x)$ gives $2(-5)^3 + 16(-5)^2 + 39(-5) + 45 = 0$, confirming $x + 5$ is a factor. Factoring $f(x)$ gives $f(x) = (x + 5)(2x^2 + 6x + 9)$.

Use the Factor Theorem to Determine Whether X - C f(x)=2x3+16x2+39x+45;c=−5f ( x ) = 2 x ^ { 3 } + 16 x ^ { 2 } + 39 x + 45 ; c = - 5f(x)=2x3+16x2+39x+45;c=−5

Use the Factor Theorem to Determine Whether X - C $f ( x ) = 2 x ^ { 3 } + 16 x ^ { 2 } + 39 x + 45 ; c = - 5$