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

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Answer 1 · 2017-07-19T13:01:56

$= (x + 1) (x + 2) (x - 2)$ $=(x+1)(x+2)(x-2)$

Group the four terms into two pairs, making sure there is a + sign between them. Then take out a common factor from each.

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

$= x^{2} (x + 1) - 4 (x + 1) \leftarrow$ $=x^2(x+1)-4(x+1)" "larr$ note the change in signs!

There is a common bracket in the two terms:

$= (x + 1) (x^{2} - 4) \leftarrow$ $=(x+1)(x^2-4)" "larr$ factor the difference of squares

$= (x + 1) (x + 2) (x - 2)$ $=(x+1)(x+2)(x-2)$

How do you determine the binomial factors of x3+x2−4x−4x^3+x^2-4x-4?