Question

How do you factor the expression `-y^2 + 9y - 20`?

Answer 1

`-(y- 4)(y - 5) = (4 - y)(y - 5) = (y - 4)(5 - 4)`

Explanation:

It is very uncomfortable working with a negative sign in the first term. Swopping the first and third terms will not help.

Divide out the negative. (actually -1), causing the signs in the bracket to change.

`-(y^2 - 9y + 20)`

Finding factors of 20 which add to 9 leads to 4 and 5.
The signs in the brackets will be the same (because of the +20), both signs will be negative (because of the -9).

This gives `-(y- 4)(y - 5)`

It can be left like this or multiplying the negative into either one of the brackets gives
`(4 - y)(y - 5) or (y - 4)(5 - 4)`