Question

How do you factor `2x² - 5x + 3`?

Answer 1

`(2x-3)(x-1)`

Explanation:

Find factors of 2 and 3 which ADD to make 5..
The signs are the same (because of +3),
both are minus (because of -5)

Find factors, cross multiply and add the answers.

2 and 3 are prime numbers so we can only combine them in 2 ways:

`(2)" "(3)" "color(white)(xxxxxxxxx)(2)" "(3)`

`2" "3 rarr1xx3=3 color(white)(xxxxxxxxx)2" "1rarr1xx1=1`
`1" "1rarr2xx1=ul2color(white)(xxxxx.xxx)1" "3rarr2xx3=ul6`
`color(white)(xxx.xxxxx)"sum" = 5color(white)(xxx.xxxxxxxx.xxxxxx)"sum" =7`

The first combination is what we need.

`(2x-3)(x-1)`