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# Factoring

Asked Jan 15, 2007, 05:12 AM — 2 Answers
How do I factor these problems

X^3-2x^2-4x-8

X^7y^2-4x^5yy^2-21x^3y^2

2 Answers
 galactus Posts: 2,272, Reputation: 1436 Ultra Member #2 Jan 15, 2007, 12:03 PM
Quote:
 ]How do I factor these problems X^3-2x^2-4x-8
This one is not easily factorable. It has 2 complex roots.

Are you sure you don't mean $x^{3}-2x^{2}-4x+8$

Otherwise, as you have it, the factorization is(which I pumped out with Maple):

$(x+\frac{14403}{17161}+\frac{23073}{19028}I)\left( x+\frac{14403}{17161}-\frac{23073}{19028}I\right)(x-\frac{63025}{17133})$

Quote:
 x^7y^2-4x^5yy^2-21x^3y^2
Is this what you mean:

$x^{7}y^{2}-4x^{5}y^{2}-21x^{3}y^{2}$?.

The why I have highlighted. I suppose it's errant?.

If this is correct, then factor out $x^{3} \;\ and \;\ y^{2}$:

$x^{3}y^{2}(x^{4}-4x^{2}-21)$

Factor in the parentheses by letting $u=x^{2}$

$(u^{2}-4u-21)=(u-7)(u+3)$

Resub:

$x^{3}y^{2}(x^{2}-7)(x^{2}+3)$
 Elisha Grey Posts: 31, Reputation: 7 Junior Member #3 Jan 17, 2007, 09:17 AM
If you mean x^3 - 2x^2 - 4x + 8, then this equals
X^2(x-2) - 4(x-2) = (x^2 - 4) (x-2) = (x+2)(x-2)^2

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