Question

How do you factor `8 - 2b - b^2`?

Answer 1

`color(green)(-1(b-2)(b+4)` is the factorised format.

Explanation:

`8 - 2b - b^2 =- (b^2 + 2b -8)`

We can Split the Middle Term of `b^2 + 2b -8` 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*-8 = -8`
and
`N_1 +N_2 = b = 2`
After trying out a few numbers we get `N_1 = 4` and `N_2 =-2`
`4*-2 = -8` and `4+(-2)= 2`

`b^2 + 2b -8 = b^2 + 4b - 2b -8`
`= b(b+4) - 2(b+4)`
`b+4` is common to both terms:
`=color(green)( (b-2)(b+4)`