Question

How do you divide `(5x ^ { 4} + 2x^3 - 9x + 12) \div ( x ^ { 2} - 3x + 4)`?

Answer 1

The quotient is `5x^2+17x+31` and the remainder is `16x-112`

Explanation:

You perform a long division

`color(white)()` `x^2-3x+4` `|` `color(white)(a)` `5x^4+2x^3+0x^2-9x+12` `color(white)(aa)` `|` `5x^2+17x+31`

`color(white)(aaaaaaaaaaaa)` `5x^4-15x^3+20x^2`

`color(white)(aaaaaaaaaaaaa)` `0+17x^3-20x^2-9x`

`color(white)(aaaaaaaaaaaaaaaa)` `17x^3-51x^2+68x`

`color(white)(aaaaaaaaaaaaaaaaa)` `-0+31x^2-77x+12`

`color(white)(aaaaaaaaaaaaaaaaaaaaa)` `+31x^2-93x+124`

`color(white)(aaaaaaaaaaaaaaaaaaaaaaaa)` `-0+16x-112`

Therefore,

`(5x^4+2x^3+0x^2-9x+12)/(x^2-3x+4)=(5x^2+17x+31)+(16x-112)/(x^2-3x+4)`