Question

What is the complete factorization of the polynomial below?

x3 - 3x2 + x - 3

Answer 1

Answer:

The complete factorization of the given polynomial is:

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

Step-by-step explanation:

Factorization of a polynomial--

It means that the polynomial could be expressed as the product of distinct factors containing the rational roots of the polynomial.

We are given a polynomial expression as:

$x^3-3x^2+x-3$

Now, it could be factorized as follows:

$x^3-3x^2+x-3=x^2(x-3)+1(x-3)\\\\i.e.\\\\x^3-3x^2+x-3=(x^2+1)(x-3)$

Now, we know that the expression:

$x^2+1$ do not have a rational root.

Hence, the complete factorization is:

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