Which are zeroes for the function f(x) = (x + 3)(x − 7)(x + 5)?

Polynomial functions are those function which consists of one or more variables with degree more than one. There are many types of polynomials like quadratic polynomial functions, cubic functions, etc.

Answer: The zeroes of the function f(x) = (x + 3)(x − 7)(x + 5) are x = -3, x = 7 and x = -5.

Let's understand the solution in detail.

Explanation:

The zeroes are those values of the variable for which the polynomial as a whole has zero value.

To find the number of zeroes in the given function, we check for f(x) = 0.

Hence, (x + 3)(x − 7)(x + 5) = 0

Now, using the zero product rule of polynomial functions, we see that:

x - 3 = 0 or x = 3

x + 7 = 0 or x = -7

x + 5 = 0 or x = -5

Hence, we have three roots in this function: 3, -7, and -5.

Thus, the zeroes of the function f(x) = (x + 3)(x − 7)(x + 5) are x = -3, x = 7 and x = -5.