Express the polynomial as a product of linear factors f(x)=x3-5x2-18x+72

 The given polynomial can be expressed as  (x-3)(x+4)(x-6).

Step-by-step explanation:  We are given to express the following cubic polynomial as a product of linear factors :

We have the factor theorem that states as follows :

FACTOR THEOREM :  If x = a is a zero of the polynomial p(x), then (x - a) is a factor of the polynomial p(x).

If x = 1, then

If x = 2, then

If x = 3, then

So, x = 3 is a zero of f(x), implies that (x - 3) is a factor of f(x).

Therefore, we have

Thus, the given polynomial can be expressed as  (x-3)(x+4)(x-6).

both equations and proportions are better.