Question

How do you use the remainder theorem to find the remainder for the division `(2x^3-3x^2-10x+3)div(x-3)`?

Answer 1

Evaluate `f(3)` The answer is the remainder.

In this case there is no remainder which means that (x-3) is a factor.

Explanation:

`(2x^3-3x^2-10x+3)divcolor(red)((x-3))`

`rarr "make " color(red)(x-3 =0, rarr x=3)`

`"Let " f(x) =2x^3-3x^2-10x+3`

`f(color(red)(3))` will give the remainder.

`f(3) = 2(3)^3-3(3)^2-10(3)+3`

`color(white)(xxxx)=54-27-30+3`

`color(white)(xxxx) = 0 " "larr " this is the remainder"`

There is no remainder.

This means that `(x-3) " is a factor of " 2x^3-3x^2-10x+3`