Thread: Factor and solve for x
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Old May 14th, 2008, 04:08 PM
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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 \\ &=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
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