Factoring a Cubic Polynomial: x^3-2x^2-5x+6

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Homework Statement



Factor the equation.

Homework Equations



x^3-2x^2-5x+6

The Attempt at a Solution



Could someone help me know how to factor this equation?
 
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peace-Econ said:

Homework Statement



Factor the equation.

Homework Equations



x^3-2x^2-5x+6

The Attempt at a Solution



Could someone help me know how to factor this equation?

The rational root theorem is a helpful place to start. One factor I found very quickly was x - 1.

BTW, your thread title doesn't seem to have much to do with your question. Is this the characteristic equation for a third-order DE?
 


You're right. I was just working on the characteristic equation. But, I could figure it out. Thank you so much!
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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