Factor and solve for x

• May 14th 2008, 02:04 PM
Jim Newt
Factor 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 PM
Moo
Quote:

Originally Posted by Jim Newt
x^3 + 5x^2 - x - 5 = 0

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

Jim

Hello,

You can see that the sum of the coefficients is 0.
Hence, 1 is a root...

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

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

Solve :)
• May 14th 2008, 02:39 PM
Krizalid
\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.)