Question

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

Answer 1

`2x^2+5x+2`

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like `ax^2 + bx + c`, we need to think of 2 numbers such that:
`N_1*N_2 = 2*2 = 4`
and
`N_1 +N_2 = b = 5`
After trying out a few numbers we get `N_1 = 4` and `N_2 =1`
`4.1= 4`, and `4+1= 5`

`2x^2+5x+2 = 2x^2+4x + 1x+2`
`2x(x+2) +1(x+2)`

`(x+2)` is common to both the terms.

`color(blue)(( 2x+1)(x+2)` is the factorised form.