How do you factor #5a^2 - 5a - 100#?

1 Answer
Jun 4, 2015

Extract the obvious numeric factor of #5# from #5a^2-5a-100# to get
#color(white)("XXXX")##5(a^2-1a-20)#

So we are looking for two numbers, #p# and #q#
such that
#color(white)("XXXX")##p+q = -1#
and
#color(white)("XXXX")##p*q = -20#

With only a little consideration of the options, we get
#color(white)("XXXX")##(4,-5)#
and the final factors are
#color(white)("XXXX")##=5(a+4)(a-5)#