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

1 Answer
Alan P.
Oct 9, 2015

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

Explanation:

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

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

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

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