SOLUTION: factor the polynomial. x^3+3x^2+2x+6

Question 989210: factor the polynomial.
x^3+3x^2+2x+6
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

If this polynomial has rational factors they must come from the set

Use synthetic division to determine the first factor. If you need a refresher on synthetic division, see Purple Math Synthetic Division Note that this section of the Purple Math website consists of four pages; read them all.

One of the divisors will work and I'll leave it up to you to find that divisor. But the quotient when you do find the correct one will be

. This polynomial does not factor over the real numbers, so if your domain is the Reals, you are done. However, the quadratic binomial does factor over the complex numbers, thus:

where

is the imaginary number defined as

John

My calculator said it, I believe it, that settles it

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