Question

How do you factor `2x^2 + 3x + 1`?

Answer 1

`2x^2 + 3x + 1`

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 = a*c = 2*1 = 2`
and,
`N_1 +N_2 = b = 3`

After trying out a few numbers we get `N_1 = 2` and `N_2 =1`
`2*1 = 2`, and `2+1= 3`

`2x^2 + 3x + 1 = 2x^2 + 2x +x + 1`
`2x(x+1) +1(x+1)`
`color(purple)((2x+1)(x+1)`