[HELP] Factoring 4 terms: x^3 - x^2 - x + 10

[Marco]

Please help me factor this x^3-x^2-x+10

I factored it by grouping so first, x^3-x^2 = x^2(x-1)
Second, -x+10 = -(x-10) and I don't know what to do next since the number inside the parenthesis are different what will I do?

Thank you in Advance for answering!

Have a nice day Sir/Ma'am

 

[ksdhart2]

One thing you might try is using the Rational Root Theoremhttp://www.purplemath.com/modules/rtnlroot.htm. That theorem tells you that the potential rational roots are of the form: \(\displaystyle \dfrac{p}{q}\), where p is any factor of the constant (i.e. last) term and q is any factor of the highest-order (i.e. first) term. In this specific case, those are:

\(\displaystyle \pm \dfrac{1,2,5,10}{1}=\pm 1, \pm 2, \pm 5, \pm 10\)

Note that these are not guaranteed to be roots of the polynomial. In fact, it's possible that none of them are. But this theorem gives you a good starting point to guess what the roots might be. If you found any, keep in mind that if a is a root of the polynomial, then (x - a) must be a factor of the polynomial. What happens if you try to use Polynomial Long Divisionhttp://www.purplemath.com/modules/polydiv2.htm to proceed?

 

[Deleted member 4993]

Please help me factor this x^3-x^2-x+10

I factored it by grouping so first, x^3-x^2 = x^2(x-1)
Second, -x+10 = -(x-10) and I don't know what to do next since the number inside the parenthesis are different what will I do?

Thank you in Advance for answering!

Have a nice day Sir/Ma'am

What are the rules that you have been taught (e.g. rational root theorem, polynomial division, etc.) to assist you in such problems?

 

[stapel]

Please help me factor this x^3-x^2-x+10

I factored it by grouping so first, x^3-x^2 = x^2(x-1)
Second, -x+10 = -(x-10) and I don't know what to do next since the number inside the parenthesis are different what will I do?

In this case, factoring "in pairs" won't work. Instead, you need to bring completely different tools to bear.

To learn the basic process for factoring polynomials (or "solving" for their roots, which uses the same methods), try here. The first step, you'll learn, is to apply the Rational Roots Test -- and to do a quick graph in your calculator, to see which of the "maybe" roots would be best to try first!