Question

Is x – 8 a factor of the function f(x) = –2x3 + 17x2 – 64? Use the Remainder Theorem to justify your answer.

Answer 1

.

SOLUTION

Applying remainder theorem;

$\begin{gathered} f(x)=-2x^3+17x^2-64 \\ \end{gathered}$

If x-a is a factor of a function f(x); then f(a)=0.

$\begin{gathered} x-8=0 \\ x=8 \end{gathered}$$\begin{gathered} f(8)=-2(8)^3+17(8)^2-64=-2(512)+17(64)-64 \\ f(8)=-1024+1088-64=-1088+1088 \\ f(8)=0 \end{gathered}$

SINCE F(8)=0, THEN X-8 IS A FACTOR OF -2X^3+17X^2-64.