Question

How do you factor `n^3+5n^2-4n-20` by grouping?

Answer 1

(n + 5)(n-2)(n+2)

Explanation:

'Group' the terms as follows:

`[n^3+5n^2]+[-4n-20]`

now factorise each group.

`rArrn^2(n+5)-4(n+5)`

There is now a common factor of (n +5) which can be taken out.

`rArr(n+5)(n^2-4)`

now `n^2-4" is a difference of squares"`

which `color(blue)" In general is factorised as follows "`

`color(red)(|bar(ul(color(white)(a/a)color(black)(a^2-b^2=(a-b)(a+b))color(white)(a/a)|)))`
`rArrn^2-4=(n-2)(n+2)`

`rArrn^3+5n^2-4n-20=(n+5)(n-2)(n+2)`