Question

Which polynomial when factored gives the zeros for the polynomial shown in the graph?

Answer 1

According to the given graph, the zeros of the function are x = -2 and x = 3 because the function intercepts there the x-axis.

Hence, the zeros are x = -2 and x = 3.

To find the correct polynomial, we evaluate the x-values above to zero which polynomial gives a zero after evaluating it.

`\begin{gathered} A\colon \\ (-2)^3+8(-2)^2+21(-2)+18=-8+32-42+18=0 \\ (3)^3+8(3)^2+21(3)+18=27+72+63+18=180 \end{gathered}`
`\begin{gathered} B\colon_{} \\ (-2)^3-2(-2)^2-9(-2)+18=-8-8+18+18=20 \end{gathered}`
`\begin{gathered} C\colon \\ (-2)^3-4(-2)^2-3(-2)+18=-8-16+6+18=0 \\ (3)^3-4(3)^2-3(3)+18=27-36-9+18=0 \end{gathered}`

As you can observe, option C is the correct answer because it's satisfied by both x = -2 and x = 3.