Question

How do you divide `3x ^ { 2} + 14x ^ { 2} + 20x + 29` by `x + 3`?

Answer 1

The remainder is `color(red)(14)` and the quotient is `=3x^2+5x+5`

Explanation:

Condtions : I assumed that the first term of the dividend is `=3x^3`

Let's perform the synthetic division

`color(white)(aa)` `-3` `color(white)(aaaaaa)` `|` `color(white)(aaa)` `3` `color(white)(aaaaaaaa)` `14` `color(white)(aaaaaaa)` `20` `color(white)(aaaaaa)` `29`
`color(white)(aaaaaaaaaaaa)` `------------`

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaaa)` `color(white)(aaaaaaa)` `-9` `color(white)(aaaaa)` `-15` `color(white)(aaaaa)` `-15`
`color(white)(aaaaaaaaaaaa)` `------------`

`color(white)(aaaa)` `color(white)(aaaaaaa)` `|` `color(white)(aaa)` `3` `color(white)(aaaaaaaaa)` `5` `color(white)(aaaaaaa)` `5` `color(white)(aaaaaaa)` `color(red)(14)`

The remainder is `color(red)(14)` and the quotient is `=3x^2+5x+5`

`(3x^3+14x^2+20x+29)/(x+3)=3x^2+5x+5+14/(x+3)`