Given:
[tex]f(x)=2x^3-5x^2-3x+16[/tex]To find:
[tex]f(-2)[/tex]Explanation:
Using the synthetic division,
Thus, the remainder is - 14.
Using the remainder theorem,
Remainder Theorem states that if polynomial f(x) is divided by a linear binomial of the form (x - a) then the remainder will be f(a).
[tex]\begin{gathered} f(-2)=2(-2)^3-5(-2)^2-3(-2)+16 \\ =-14 \end{gathered}[/tex]Thus, the remainder is - 14.
Final answer:
The remainder is - 14.
