How do you determine the binomial factors of #x^3+4x^2-x-4#?

1 Answer
Shwetank Mauria
Dec 14, 2016

#x^3+4x^2-x-4=(x-1)(x+1)(x+4)#

Explanation:

It is apparent from the given polynomial #x^3+4x^2-x-4#, that if #x^2# is taken from first two terms, we have #x+4# left out and this is also left out if take out #-1# from remaining two terms.

Hence #x^3+4x^2-x-4#

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

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

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

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

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

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