How do you factor the trinomial #20x^2-13x-15#?

1 Answer
George C.
May 12, 2016

#20x^2-13x-15=(5x+3)(4x-5)#

Explanation:

Use an AC method:

Find a pair of factors of #AC=20*15=300# which differ by #B=13#.

Since #300# is divisible by #5^2# and #13# is not divisible by #5#, one of the factors must be divisible by #25# in order that the other is not divisible by #5#.

With this condition in mind, we quickly find the pair #25, 12# works in that #25*12 = 300# and #25-12 = 13#

Use this pair to split the middle term and factor by grouping:

#20x^2-13x-15#

#=20x^2-25x+12x-15#

#=(20x^2-25x)+(12x-15)#

#=5x(4x-5)+3(4x-5)#

#=(5x+3)(4x-5)#

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