Question

Express the polynomial as a product of liner factors

Answer 1

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

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.