Use the Factor Theorem to determine whether x - c is a factor of f(x).
-$$f ( x ) = 7 x ^ { 3 } + 33 x ^ { 2 } - 9 x + 5 ; x + 5$$
A)Yes
B)No

Question

Quizplus · Accepted Answer

To determine if $x + 5$ is a factor of $f(x) = 7x^3 + 33x^2 - 9x + 5$, we use the Factor Theorem by evaluating $f(-5)$. If $f(-5) = 0$, then $x + 5$ is a factor. Substituting $-5$ into $f(x)$ gives $f(-5) = 7(-5)^3 + 33(-5)^2 - 9(-5) + 5 = -875 + 825 + 45 + 5 = 0$. Since $f(-5) = 0$, $x + 5$ is indeed a factor of $f(x)$.

Use the Factor Theorem to Determine Whether X - C f(x)=7x3+33x2−9x+5;x+5f ( x ) = 7 x ^ { 3 } + 33 x ^ { 2 } - 9 x + 5 ; x + 5f(x)=7x3+33x2−9x+5;x+5

Use the Factor Theorem to Determine Whether X - C $f ( x ) = 7 x ^ { 3 } + 33 x ^ { 2 } - 9 x + 5 ; x + 5$