Write a polynomial function in standard form with the given zeroes:

x=-1/2, 0, 4

My equation is p(x)=x(2x+1)(x+0)(x-4)
Is that right? If so, can you explain how to multipy this out correctly.

Thanks in advance.

Yes, your equation is correct. To multiply the polynomial expression correctly, you'll need to follow a few steps:

1. Start by multiplying the binomials together following the distributive property.
p(x) = x(2x+1)(x+0)(x-4)
= x(2x^2 + x)(x^2 - 4x)

2. Next, use the distributive property to multiply each term in the first set of parentheses (2x^2 + x) by each term in the second set of parentheses (x^2 - 4x).
p(x) = x(2x^2 + x)(x^2 - 4x)
= x * 2x^2 * (x^2 - 4x) +
x * x * (x^2 - 4x)

3. Simplify each term by multiplying the coefficients and adding the exponents.
p(x) = 2x^3 * (x^2 - 4x) +
x^2 * (x^2 - 4x)

4. Continue simplifying by distributing the remaining terms.
p(x) = 2x^5 - 8x^4 + x^4 - 4x^3
= 2x^5 - 7x^4 - 4x^3

Thus, the polynomial function in standard form with the given zeroes is p(x) = 2x^5 - 7x^4 - 4x^3.