Express the polynomial as a product of liner factors

A. (x-3)(x+4)(x-6)

Step-by-step explanation:

We need to find the polynomial f(x)=x^3 - 5x^2 - 18x + 72 as a product of lineal factors.

We're going to solve the problem using Ruffini's rule:

                 1        -5         -18       72

3                          3          -6       -72

                   1       -2         -24         0

Then we have:

                 1       -2         -24

-4                       -4          24

                 1        -6         0

Lastly:

                  1        -6

6                            6

                 1            0

Then, the roots are: x=6, x=-4 and x=3

For that reason, the product of linear factors is:

(x-6)(x+4)(x-3) which is option A.

step-by-step explanation: