Question

How do you factor the expression `2x^2+ 5x + 3`?

Answer 1

`(2x+3)(x+1)`

Explanation:

When you want to factorise a quadratic expression, each part conveys information. `color(red)(2) x^2 color(green)+ color(yellow)(5)x color(blue)(+) color(red)3`

Match the colours to the information it conveys.

Find the factors of `color(red)(2) and color(red)(3)` which `color(blue)(ADD)` together to give `color(yellow)5`.
The signs in the brackets will be the `color(blue)(SAME)`, they are both `color(green)(positive)`.

`2 x 3` `rArr 1 xx 3 = 3`
`1 x 1` `rArr 2 xx 1 = 2` `3+2=5`

`(2x+3)(x+1)`