Answer:
I believe it's C.
Explanation:
The correct equation of p is C. p(x) = x(x - 3)^2(2x + 7)^2. This is because the given polynomial has a zero of multiplicity 2 at x = 3, a zero of multiplicity 1 at x = 0, and a zero of multiplicity 2 at x = -7/2. Therefore, the equation of the polynomial can be written as p(x) = k(x - 3)^2(x)(2x + 7)^2, where k is some constant. Since the leading coefficient of the polynomial is 1, k = 1. Thus, we get the equation p(x) = x(x - 3)^2(2x + 7)^2.
It is option C and not A, B, or D because:
Option A, p(x)= x(x - 3)(2x + 7)^2, has only one factor of (x - 3), but the given polynomial has a factor of (x - 3) squared.
Option B, p(x) x^2(x - 3)(2x + 7), has an extra factor of x^2 that is not present in the given polynomial.
Option D, p(x)= x(x - 3)^2(2x + 7), is very close to the correct answer, but it is missing the factor of (x) that is present in the given polynomial.
Thus, the correct equation of p is C, p(x) = x(x - 3)^2(2x + 7)^2, which includes all the necessary factors and satisfies the given conditions.
Hope this helps you! I'm sorry if it doesn't. If you need more help, ask me! :]