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

Given:

The function is:

To find:

The remainder when the given function is divided by .

Solution:

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

We have,

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

Putting in the given function, we get

Therefore, the remainder is 15.

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part a: 1.08

part b: 27.59