Question

How do you completely factor `x^3-x^2-14x+25` given x-3 is one of the factors?

Answer 1

`x-3` is not a factor.

Explanation:

Factor `x^3-x^2-14x+25` given `x-3` is a factor.

Use synthetic division.

`3|1color(white)(aa)-1color(white)(aa)-14color(white)(aaa)25`
`color(white)(aa)darrcolor(white)(aaaa)3color(white)(aaaaa)6color(white)(a)-24`
`color(white)(aaa)`--------------------------------
`color(white)(aaa)1color(white)(a^22aa)2color(white)(a^2a)-8color(white)(aaa)1`

The remainder is 1 instead of zero, so `x-3` is not a factor.

Perhaps the `25` was a typo, and should have been a `24`.