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

2 Answers
Jun 21, 2018

Answer:

#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)#

Jun 21, 2018

Answer:

#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)#