Question

How do you use synthetic division to divide `( x^4 + 3x^3 - 5x^2 + 9 ) / ( x + 3 )`?

Answer 1

The remainder is `=-37` and the quotient is `x^3-5x+15`

Explanation:

Let's perform the synthetic division

`color(white)(aaaa)` `-3` `|` `color(white)(aaaa)` `1` `color(white)(aaaa)` `3` `color(white)(aaaaaa)` `-5` `color(white)(aaaaa)` `0` `color(white)(aaaaaa)` `9`

`color(white)(aaaaaaa)` #|color(white)(aaaa)# #color(white)(aaa)-3# `color(white)(aaaaaaa)` `0` `color(white)(aaaaa)` `15` `color(white)(aaaa)` `-45`

`color(white)(aaaaaaaaa)` _________________________________________________________##

`color(white)(aaaaaaa)` #|color(white)(aaaa)# `1` `color(white)(aaaa)` `0` `color(white)(aaaaaa)` `-5` `color(white)(aaaa)` `15` `color(white)(aaaa)` `color(red)(-36)`

The remainder is `=-37` and the quotient is `x^3-5x+15`

`(x^4+3x^3-5x^2+0x+9)/(x+3)=(x^3-5x+15)-36/(x+3)`