Answer:
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
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1 -2 -24 0
Then we have:
1 -2 -24
-4 -4 24
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1 -6 0
Lastly:
1 -6
6 6
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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.
