Final answer:
The value of m is 3.
Step-by-step explanation:
A polynomial equation is an equation involving a polynomial, which is an expression consisting of variables and coefficients that involve only the operations of addition, subtraction, multiplication, and non-negative integer exponents.
To determine the value of m if g(x) = 3x³ - m * x² has x = 3 as one of its roots, we can use the concept of polynomial equations. When x = 3 is a root of g(x), it means that when we substitute x = 3 into the equation, the equation will equal 0. Therefore, we can set up the equation 3(3)³ - m * (3)² = 0 and solve for m:
27 - 9m = 0
9m = 27
m = 3
So, the value of m is 3.