Question

How do you divide `(4x^3 - 8x^2 + 7x - 9) ÷ (x + 3)`?

Answer 1

The quotient is `=(4x^2-20x+67)` and the remainder is `=-210`

Explanation:

You can do a long division

`color(white)(aaaa)` `4x^3-8x^2+7x-9` `∣` `x+3`

`color(white)(aaaa)` `4x^3+12x^2` `color(white)(aaaaaaa)` `∣` `4x^2-20x+67`

`color(white)(aaaaaa)` `0-20x^2+7x`

`color(white)(aaaaaaaa)` `-20x^2-60x`

`color(white)(aaaaaaaaaaa)` `+0+67x-9`

`color(white)(aaaaaaaaaaaaaaa)` `+67x+201`

`color(white)(aaaaaaaaaaaaaaaaaaa)` `0-210`

The quotient is `=(4x^2-20x+67)`

and the remainder is `=-210`

You can get the remainder directly with the remainder theorem

Let `f(x)=4x^3-8x^2+7x-9`

Then, `f(-3)=4*(-3)^3-8(-3)^2+7(-3)-9`

`=-108-72-21-9=-210`

This is the remainder.