Question

How do you factor completely: `x^2 − 3x − 28`?

Answer 1

`=color(blue)((x+4)(x-7)`

Explanation:

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 = 1*-28 = -28`
and
`N_1 +N_2 = b = -3`

After trying out a few numbers we get `N_1 = -7` and `N_2 =4`
`7*-4 = -28`, and `4+(-7)= -3`

`x^2 -3x -28`
`=x^2 -7x +4x -28`
`=x(x-7)+ 4(x -7)`

`=color(blue)((x+4)(x-7)`