Factorization of a real polynomial

Question

Can I factor univariate polynomials with real coefficients as a product of quadratic trinomials and binomials corresponding to the complex conjugate and real roots using Wolfram Alpha ?

E.g.,

$$x^3-2x^2+x-2=(x^2+1)(x-2)$$

Answer 1

If I understood you correctly, you want a factorization over the reals. One way to do this is to use decimals for your coefficients. For example, for your question you can use

Factor[x^3 - 3.0* x^2 - 2.0]

which WA will return

(1 x - 2) (1 x^2 + 1)

For the other example you tried, $x^4 - 2 x^2 + x - 2$, the command

Factor[x^4-2.0*x^2+x-2.0]

will return

(x - 1.49257) (x + 1.78537) (x^2 - 0.292798 x + 0.750527)

This will work well if there are only rational roots, but for irrational roots you might need to do extra work to get enough precision.

Answer 2

Putting the LHS into Wolfram Alpha gets you the form you want, about half way down the page under "Alternate forms". If that isn't what you want then I don't understand the question.

Answer 3

Yes, you can do it, using keyword "factor".

For example, Wolfram Alpha Pro returns for $factor x^4-2x^2+x-2:$