name all zeros for f(x)=x^2(x-1)^2(x+2)^3?

Question

please help me understand this math problem!!!

Answer 1

f(x)=x^2(x-1)^2(x+2)^3?

When f(x) = 0,

x^2(x-1)^2(x+2)^3 = 0

therefore x = 0, x = 1, x = -2

3 solutions to x

Answer 2

If a function f(x) is written as the product of multiple expressions, the zeroes of each expression are also zeroes of the function, since zero times anything is also zero. You need to solve for each factor equal to zero.

x^2 = 0 ==> x = 0
(x - 1)^2 = 0 ==> x - 1 = 0 ==> x = 1
(x + 2)^3 = 0 ==> x + 2 = 0 ==> x = -2

So the zeroes are 0, 1, and -2. 0 and 1 are double roots and -2 is a triple root.

Answer 3

x^2 * (x-1)^2 * (x+2)^3 = f(x) = 0
therefore, x^2=0, (x-1)^2 = 0, (x+2)^3 = 0
x =0, (x-1) = 0, (x+2) = 0
x=0, x=1, x=-2