Question

How do you factor `21n ^ { 2} + 3n - 24`?

Answer 1

`3(n-1)(7n+8)`

Explanation:

`"take out a "color(blue)"common factor "3`

`=3(7n^2+n-8)`

`"factor the quadratic using the a-c method"`

`"the factors of the product "7xx-8=-56`

`"which sum to "+1" are "-7" and "+8`

`"split the middle term using these factors"`

`7n^2-7n+8n-8larrcolor(blue)"factor by grouping"`

`=color(red)(7n)(n-1)color(red)(+8)(n-1)`

`"take out the "color(blue)"common factor "(n-1)`

`=(n-1)(color(red)(7n+8))`

`21n^2+3n-24=3(n-1)(7n+8)`

Answer 2

`21*(n-1)(n+8/7)`

Explanation:

Solving the equation`21n^2+3n-24=0`
by the quadratic Formula we get

`n_(1,2)=-1/14pm15/14`
so
`n_1=1`
`n_2=-8/7`
and we get
`21(n-1)(n+8/7)`