Find the zeroes of each function. State the multiplicity of multiple zeroes.

y=(x+3)^3

y=x(x-1)^3

I know you're supposed to factor them out, but I'm really not sure how to. Thanks.

The equations are already factored out. For the first one, y is zero at x=3 only. For the second equation, y = 0 when x = 0 or 1.

The multiplicity of the zeroes that come from cubed factors is 3.

To find the zeroes of a function, you need to find the values of x that make the function equal to zero. In this case, the functions are already factored, which makes it easier to identify the zeroes.

For the first function, y = (x+3)^3, the function will be equal to zero when (x+3) = 0. Solving for x, you subtract 3 from both sides of the equation giving you x = -3. Therefore, the zero for this function is x = -3.

For the second function, y = x(x-1)^3, the function will be equal to zero when either x = 0 or (x-1) = 0. Solving for x, you find x = 0 and x = 1. Therefore, the zeroes for this function are x = 0 and x = 1.

Now, let's talk about the concept of multiplicity. The multiplicity of a zero refers to how many times that zero is a solution to the equation. In this case, both equations have cubed factors.

For the first function, y = (x+3)^3, the zero x = -3 has a multiplicity of 3. This means that the factor (x+3) is repeated three times in the equation.

For the second function, y = x(x-1)^3, the zeroes x = 0 and x = 1 have multiplicities of 1 and 3, respectively. This means that the factor (x-1) is repeated three times for the zero x = 1, but the factor x is not repeated at all for the zero x = 0.

Therefore, the zeroes of the first function are x = -3 with a multiplicity of 3, and the zeroes of the second function are x = 0 with a multiplicity of 1, and x = 1 with a multiplicity of 3.