Provide an appropriate response.
-Suppose that $\mathrm { f }$ is a polynomial function of degree 4 . If $- 5$ and 11 are zeros of $f$ and the graph of $f$ is symmetric with respect to the $y$-axis, write $f ( x )$ in factored form.
A) $f ( x ) = ( x + 5 ) ^ { 2 } ( x - 11 ) ^ { 2 }$
B) $f ( x ) = ( x + 5 ) ( x - 11 ) ( x - 5 ) ( x + 11 )$
C) $f ( x ) = ( x + 5 ) ( x - 11 )$
D) $f ( x ) = ( x - 5 ) ^ { 2 } ( x + 11 ) ^ { 2 }$

Question

Quizplus · Accepted Answer

Since the graph of $f$ is symmetric with respect to the $y$-axis and $-5$ and $11$ are zeros, their symmetric counterparts $5$ and $-11$ must also be zeros. Thus, $f(x)$ must have factors $(x + 5)$, $(x - 11)$, $(x - 5)$, and $(x + 11)$, making it a degree 4 polynomial.

Provide an Appropriate Response f\mathrm { f }f Is a Polynomial Function of Degree 4

Provide an Appropriate Response $\mathrm { f }$ Is a Polynomial Function of Degree 4