Question

How do you factor `5x^2 + 17x + 6`?

Answer 1

`(5x+2)(x+3)`

Explanation:

Find factors of `5 and 6` whose products ADD to `17`

It might take a bit of trial and error to find the correct combination of factors.

`color(white)(........)5 and 6`
`color(white)(.......)darr" "darr`
`color(white)(........)5 " " 2" "rarr 1 xx 2=2`
`color(white)(........)1 " " 3" "rarr 5 xx 3=ul15`
`color(white)(...............................................)17`

The rows above give the two factors:

`(5x+2)(x+3)`