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)