Question

F(x)=(x-6)^3(x+9)^2 zeroes

Answer 1

Answer: The zeroes of the function
`\(f(x) = (x-6)^3(x+9)^2\)` are
`\(x = 6\)` and
`\(x = -9\)`.

Explanation:

The zeroes of a polynomial are the x-values that make the polynomial equal to zero. For the given function
`\(f(x) = (x-6)^3(x+9)^2\)`, the zeroes are the values of x that satisfy the equation
`\(f(x) = 0\)`.

Looking at the factors of the polynomial, we can see that the zeroes are:

-
`\(x = 6\)`, because if we substitute
`\(x = 6\)` into the function, we get
`\((6-6)^3(6+9)^2 = 0\)`.

-
`\(x = -9\)`, because if we substitute
`\(x = -9\)` into the function, we get
`\((-9-6)^3(-9+9)^2 = 0\)`.

So, the zeroes of the function
`\(f(x) = (x-6)^3(x+9)^2\)` are
`\(x = 6\)` and
`\(x = -9\)`.