Question

Determine the roots, describe the end behavior, and draw a quick sketch of thepolynomial defined by f(x) = - 3x5 + 6x?

Answer 1

$\begin{gathered} f(x)=-3x^5+6x^3 \\ -3x^5+6x^3=-3x^3(x^2-2) \\ -3x^3(x^2-2)=0 \\ -3x^3=0 \\ x^3=0 \\ x=0 \\ \\ x^2-2=0 \\ x^2=2 \\ \sqrt[]{x^2}=\sqrt[]{2} \\ x=\pm\text{ }\sqrt[]{2} \\ \text{The roots of the polynomial }f(x)=-3x^5+6x^3\text{ are 0 and }\pm\text{ }\sqrt[]{2} \end{gathered}$