Question

How do you factor `6 + 7x - 20x^2`?

Answer 1

`6-7x-20x^2 = (3-4x)(2+5x)`

Explanation:

Find factors of `6 and 20` which differ by `7`

`" "6" "20`
`" "darr" "darr`

`" "3" "4" "rarr 2 xx 4 = 8`
`" "2" "5" " rarr 3xx5 =ul15`
`color(white)(xxxxxxxxxxxxxxxxx)7`

We have the correct factors, now add in the signs.

We need `-20` and `+7`

`" "3" "-4" "rarr 2 xx -4 = -8`
`" "2" "+5" " rarr 3xx+5 =+ul15`
`color(white)(xxxxxxxxxxxxxxxxxxxxx)+7`

`6-7x-20x^2 = (3-4x)(2+5x)`