Question

How do you divide `( 3x^3 - 5x^2 + 10x +4 )/(3x+1)`?

Answer 1

The answer is `=x^2-2x+4`

Explanation:

Let's do the long division
`color(white)(aaa)` `3x^3-5x^2+10x+4` `color(white)(aaa)` `∣` `3x+1`
`color(white)(aaa)` `3x^3+x^2` `color(white)(aaaaaaaaaaaaa)` `∣` `x^2-2x+4`
`color(white)(aaaa)` `0-6x^2+10x`
`color(white)(aaaaaaa)` `-6x^2-2x`
`color(white)(aaaaaaaaaa)` `0+12x+4`
`color(white)(aaaaaaaaaaaa)` `+12x+4`
`color(white)(aaaaaaaaaaaaaa)` `+0+0`

`:.(3x^3-5x^2+10x+4)/(3x+1)=x^2-2x+4`