Roots of polynomial function

Question

Which of the following best describes the roots of the polynomial function f(x)=(x+2)^2(x-4)(x+1)^3?

Answer 1

As Peter explained, the roots are -2, 4, and -1.

The multiplicity of -2 is 2 because of the square

The multiplicity of 4 is 1

The multiplicity of -1 is 3 because of the cube

Answer 2

When a polynomial is factored, setting each factor = 0 will get the roots.

By inspection roots here would be x = -2 (twice), 4, -1 (3 times)

Answer 3

Brianna, the "roots" of a function are those values in the domain that make it's value zero. The roots of this function, f(x), appear to be -2, since the factor (x+2)^2 = 0 in this case, and 4, since the factor (x-4) = 0 in that case, and -1 since the factor (x+1)^3 = 0 in that case.

So, if you plug in any of the values -2, 4, or -1, one of the polynomial's factors becomes zero and the whole function will evaluate to zero.

"Best describes" might have to do with the multiplicity of the roots but your "following" answers are not shown.