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

##### 2 Answers

Jun 21, 2018

#### 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)#

Jun 21, 2018

#### Explanation:

Solving the equation

by the quadratic Formula we get

so

and we get