Question

How do you factor `5x^2+15x+10`?

Answer 1

`5x^2 +15x +10`

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 = 5*10 = 50`
and,
`N_1 +N_2 = b = 15`

After trying out a few numbers we get `N_1 = 10` and `N_2 =5`
`10*5 = 50`, and `10 + 5= 15`

`5x^2 +15x +10 = 5x^2 +10x + 5x +10`

`= 5x(x+2) + 5(x +2)`

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

`color(green)((5x+5)(x+2)` , is the factorised form.