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.