x^3 + 5x^2 - x - 5 = 0

Could someone point me in the right direction as to factor and solve for x? Thanks,

Jim

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- May 14th 2008, 02:04 PMJim NewtFactor and solve for x
x^3 + 5x^2 - x - 5 = 0

Could someone point me in the right direction as to factor and solve for x? Thanks,

Jim - May 14th 2008, 02:08 PMMoo
Hello,

You can see that the sum of the coefficients is 0.

Hence, 1 is a root...

-> $\displaystyle x^3+5x^2-x-5=(x-1)P(x)$

$\displaystyle \begin{aligned} x^3+5x^2-x-5 &=x^3-x^2+x^2+5x^2-x-5 \\

&=x^2(x-1)+6x^2-x-5 \\

&=x^2(x-1)+6x^2-6x+6x-x-5 \\

&=x^2(x-1)+6x(x-1)+5(x-1) \\

&=(x-1)(x^2+6x+5)

\end{aligned}$

Hence $\displaystyle x^3+5x^2-x-5=(x-1)(x+1)(x+6)$

Solve :) - May 14th 2008, 02:39 PMKrizalid
$\displaystyle \begin{aligned}

x^{3}+5x^{2}-x-5&=x^{2}\left( x+5 \right)-(x+5) \\

& =(x+5)\left( x^{2}-1 \right) \\

& =(x+5)(x+1)(x-1).

\end{aligned}$

(Slight typo at the end Moo.)