Question

Select the polynomial functions for which (x+3) is a factor. Select all that apply.

Answer 1

If x+3 is a factor, then the result of replacing x=-3 in each equation would be 0.

Replacing x=-3 in the polynomials, we have:

Option A

`\begin{gathered} f(-3)=(-3)^4-12(-3)^3+54(-3)^2-108(-3)+81=1296\text{ } \\ \text{ We see that option A is incorrect.} \end{gathered}`

Option B

`\begin{gathered} f(-3)=(-3)^4-3(-3)^3-(-3)+3=168\text{ } \\ \text{We see that option B is incorrect.} \end{gathered}`

Option C

`\begin{gathered} f(-3)=(-3)^5+2(-3)^4-23(-3)^3-60(-3)^2=0\text{ } \\ \text{We see that option C is correct.} \end{gathered}`

Option D

`\begin{gathered} f(-3)=(-3)^5+5(-3)^4-3(-3)^3-29(-3)^2+2(-3)+24=0\text{ } \\ \text{We see that option D is correct.} \end{gathered}`

The answers are options C and D.