How do you factor $x^{3} + 5 x^{2} - 9 x - 45$ $x^3 +5x^2-9x-45$ ?

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How do you factor $x^{3} + 5 x^{2} - 9 x - 45$ $x^3 +5x^2-9x-45$ ?

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Answer 1 · 2015-10-09T13:06:56

$(x + 3) (x - 3) (x + 5)$ $(x+3)(x-3)(x+5)$

Explanation:

Note that $(- 9 x - 45) = (- 9) (x + 5)$ $(-9x-45)= (-9)color(blue)((x+5))$
and that $(x^{3} + 5 x^{2}) = (x^{2}) (x + 5)$ $(x^3+5x^2) = (x^2)color(blue)((x+5))$

We can write
$x^{3} + 5 x^{2} - 9 x - 45$ $x^3+5x^2-9x-45$
$XXX = (x^{2} - 9) (x + 5)$ $color(white)("XXX")=(x^2-9)color(blue)((x+5))$

If we further note that $(x^{2} - 9)$ $(x^2-9)$ is the difference of squares $(x + 3) (x - 3)$ $color(green)((x+3))color(brown)((x-3))$
we can expand this to
$x^{3} + 5 x - 9 x - 45$ $x^3+5x-9x-45$
$XXX = (x + 3) (x - 3) (x + 5)$ $color(white)("XXX")=color(green)((x+3))color(brown)((x-3))color(blue)((x+5))$

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How do you factor $x^{3} + 5 x^{2} - 9 x - 45$ $x^3 +5x^2-9x-45$ ?

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Explanation:

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How do you factor x^3 +5x^2-9x-45x3+5x2−9x−45x^3 +5x^2-9x-45?

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How do you factor $x^{3} + 5 x^{2} - 9 x - 45$ $x^3 +5x^2-9x-45$ ?