How do you write #P(x) = x^3 − 27x − 54# in factored form?

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Answer 1 · 2018-04-18T02:16:42

#x^3-27x-54=(x-6)(x+3)^2#

#x^3-27x-54#

First note that #P(-3)=0#. This means that #x+3# is a factor of #P(x)#. Lets synthetically divide #P(x)# by #x+3# and see what remains.

#x^3-27x-54=x^3+3x^2-3x^2-9x-18x-54#

#=x^2(x+3)-3x(x+3)-18(x+3)#

#=(x^2-3x-18)(x+3)#

#=(x-6)(x+3)(x+3)#

#=(x-6)(x+3)^2#