How do you factor #4x^3+13x^2-13x-4 #?

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Answer 1 · 2015-06-08T18:21:43

Notice that the sum of the coefficients is zero, so #1# is a zero:

#f(x) = 4x^3+13x^2-13x-4#

#f(1) = 4+13-13-4 = 0#

So #(x-1)# is a factor.

#f(x) = (x-1)(4x^2+17x+4)#

#= (x-1)(4x^2+1x+16x+4)#

#= (x-1)(x*(4x+1)+4*(4x+1))#

#=(x-1)(x+4)(4x+1)#