How do you factor #5c^2 + 12c + 7#?

1 Answer
Jun 30, 2015

Answer:

Use the #a*c# method of factoring.

Explanation:

#5c^2+12c+7# is in the form #ax^2+bx+c#, where #a=5;# #b=12; and# #c=7#.

Multiply #a*c#, and find two factors that when added equal #b#.

#a*c=5*7=35#

Find two factors of #35# that when added equal #12#.

#5# and #7# fit the criteria. #5+7=12#

Rewrite #12c# as #5c# and #7c#.

Rewrite the expression.

#5c^2+5c+7c+7#

Divide the expression into two groups.

#(5c^2+5c)+(7c+7)#

Factor out the #5c# from the first group, and the #7# from the second group.

#5c(c+1)+7(c+1)#

Factor out the common term #(c+1)#.

#(c+1)(5c+7)#