Question

Find the remainder when f(x) is divided by g(x) given that f(x) = 4x3 − 5x2 − 3x + 2 and g(x) = x − 3.

Answer 1

Given:

`f(x)=4x^3-5x^2-3x+2`

`g(x)=x-3`

To find:

The remainder when f(x) is divided by g(x).

Solution:

According to remainder theorem, if f(x) is divides by (x-c), then remainder is f(c).

Using remainder theorem, if
`f(x)=4x^3-5x^2-3x+2` is divides by
`g(x)=x-3`, then remainder is f(3).

Substitute x=3 in f(x).

`f(3)=4(3)^3-5(3)^2-3(3)+2`

`f(3)=4(27)-5(9)-9+2`

`f(3)=108-45-7`

`f(3)=56`

Therefore, the required remainder is 56.