Question

Use synthetic division and remiander theorem to find f(-2) f(x)=2x^3-5x^2-3x+16

Answer 1

Given:

`f(x)=2x^3-5x^2-3x+16`

To find:

`f(-2)`

Step-by-step 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).

`\begin{gathered} f(-2)=2(-2)^3-5(-2)^2-3(-2)+16 \\ =-14 \end{gathered}`

Thus, the remainder is - 14.

Final answer:

The remainder is - 14.