Write an expanded polynomial equation based on the following information. A cubic function with a zero x=3 (with multiplicity 2), a zero at x=2, and a constant term of 18.
see related questions below. Recall that if a is a root, (x-a) is a factor.
To write an expanded polynomial equation based on the given information, we start by considering the fact that the function has a zero at x = 3 with multiplicity 2. This means that (x - 3) appears twice as a factor.
Additionally, we know that the function has a zero at x = 2, so (x - 2) is another factor.
Finally, we are given that the constant term is 18. This means that when x = 0, the function evaluates to 18. We can represent this as the product of (x - 0), or simply x, with a constant value of 18.
Combining all the information, we can express the expanded polynomial equation as follows:
f(x) = (x - 3)(x - 3)(x - 2)(x) = (x - 3)^2(x - 2)(x)
Expanding this equation further would involve multiplying all the terms together, which would result in a polynomial expression.