How do you factor #25x^2-10x-15#?

1 Answer
George C.
Apr 1, 2016

#25x^2-10x-15 = 5(x-1)(5x+3)#

Explanation:

First note that all of the terms are divisible by #5# so separate that out as a factor first:

#25x^2-10x-15 = 5(5x^2-2x-3)#

Next notice that the sum of the coefficients of the remaining factor is zero. That is: #5-2-3 = 0#. So #x=1# is a zero and #(x-1)# a factor:

#5x^2-2x-3 = (x-1)(5x+3)#

Putting it all together:

#25x^2-10x-15 = 5(x-1)(5x+3)#

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