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Math Help - Factor and solve for x

  1. #1
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    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
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  2. #2
    Moo
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    Quote Originally Posted by Jim Newt View Post
    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 \\<br />
&=x^2(x-1)+6x^2-x-5 \\<br />
&=x^2(x-1)+6x^2-6x+6x-x-5 \\<br />
&=x^2(x-1)+6x(x-1)+5(x-1) \\<br />
&=(x-1)(x^2+6x+5)<br />
\end{aligned}

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

    Solve
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  3. #3
    Math Engineering Student
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    \begin{aligned}<br />
   x^{3}+5x^{2}-x-5&=x^{2}\left( x+5 \right)-(x+5) \\ <br />
 & =(x+5)\left( x^{2}-1 \right) \\ <br />
 & =(x+5)(x+1)(x-1).<br />
\end{aligned}

    (Slight typo at the end Moo.)
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