What is the factorization of the polynomial #x^2-5x-36#?

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Answer 1 · 2016-03-11T00:43:40

#x^2-5x-36 = (x-9)(x+4)#

Find a pair of factors of #36# which differ by #5#.

The pair #9, 4# works.

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Hence we find:

#x^2-5x-36 = (x-9)(x+4)#

Alternative Method

Alternatively, complete the square then use the difference of squares identity:

#a^2-b^2=(a-b)(a+b)#

with #a=x-5/2# and #b=13/2# as follows:

#x^2-5x-36#

#=x^2-5x+25/4-25/4-36#

#=(x-5/2)^2-169/4#

#=(x-5/2)^2-(13/2)^2#

#=((x-5/2)-13/2)((x-5/2)+13/2)#

#=(x-9)(x+4)#