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).

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: