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

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

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Answer 1 · 2016-12-14T15:27:25

$x^{3} + 4 x^{2} - x - 4 = (x - 1) (x + 1) (x + 4)$ $x^3+4x^2-x-4=(x-1)(x+1)(x+4)$

Explanation:

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

Hence $x^{3} + 4 x^{2} - x - 4$ $x^3+4x^2-x-4$

= $x^{2} (x + 4) - 1 (x + 4)$ $x^2(x+4)-1(x+4)$

= $(x^{2} - 1) (x + 4)$ $(x^2-1)(x+4)$

= $(x^{2} + x - x - 1) (x + 4)$ $(x^2+x-x-1)(x+4)$

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

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

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

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