Given that p(-3)=0,p(-1)=0,and p(5)=0, which expression could be p(x)

To find an expression that represents the polynomial function p(x) given the three points (-3, 0), (-1, 0), and (5, 0), we can start by considering the fact that a polynomial of degree n will have at most n distinct solutions.

Since p(-3) = 0, it means that (x + 3) is a factor of p(x). Similarly, p(-1) = 0 implies that (x + 1) is a factor of p(x), and p(5) = 0 implies that (x - 5) is a factor of p(x).

We can multiply these factors together to obtain a polynomial expression that satisfies all three conditions:

p(x) = (x + 3)(x + 1)(x - 5)

Expanding this expression will give us the desired polynomial.

Since the polynomial p(x) equals 0 when x is -3, -1, and 5, we can construct an expression using the factors (x + 3), (x + 1), and (x - 5). This is because when these factors are multiplied together, they result in a polynomial that equals zero at those given values. Therefore, an expression that could represent p(x) is:

p(x) = (x + 3)(x + 1)(x - 5)

You are given three of the x-intercepts of p(x)

So in it simplest form

p(x) = (x+3)(x+1)(x-5)

confirmation: https://www.wolframalpha.com/input/?i=plot+p(x)+%3D+(x%2B3)(x%2B1)(x-5)

other version could be
p(x) = 14(x+3)(x+1)(x-5)
p(x) = (x+3)(x+1)(x-5)(x+9)
p(x) = (x+3)^2(x+1)(x-5) , etc