Question

Find the remainder when f(x)=2x3+2x2−3x−3 is divided by x−2.

Answer 1

Given:

The function is:

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

To find:

The remainder when the given function is divided by
`x-2`.

Solution:

According to the remainder theorem, if a polynomial P(x) is divided by (x-c), then the remainder is P(c).

We have,

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

This function is divided by
`x-2`. By using the remainder theorem, the remainder is f(2).

Putting
`x=2` in the given function, we get

`f(2)=2(2)^3+2(2)^2-3(2)-3`

`f(2)=2(8)+2(4)-6-3`

`f(2)=16+8-9`

`f(2)=15`

Therefore, the remainder is 15.