What is a cubic polynomial function in standard form with zeros 3,-4, and 5?

To find the cubic polynomial function in standard form with the given zeros (3, -4, and 5), we follow these steps:

Step 1: Use the fact that the zeros of the polynomial are the values where the polynomial equals zero. The polynomial can be written in factored form as:
f(x) = a(x - 3)(x + 4)(x - 5)

where "a" is a constant that can be chosen. If no other information is provided, we can assume a = 1 for simplicity.

Step 2: Expand the factored form.
Start by multiplying the first two factors:

(x - 3)(x + 4) = x^2 + 4x - 3x - 12 = x^2 + x - 12

Now, multiply this result by the third factor (x - 5):

(x^2 + x - 12)(x - 5) = x^3 - 5x^2 + x^2 - 5x - 12x + 60 = x^3 - 4x^2 - 17x + 60

Step 3: Write the final polynomial in standard form.
So, the cubic polynomial is:

f(x) = x^3 - 4x^2 - 17x + 60

This is the cubic polynomial in standard form with the given zeros.