Which of the following describes the roots of the polynomial function f(x)= (x+2)^2(x+4)(x+1)^3? –2 with multiplicity 2, 4 with multiplicity 1, and –1 with multiplicity 3 –2 with multiplicity 3, 4 with multiplicity 2, and –1 with multiplicity 4 2 with multiplicity 2, –4 with multiplicity 1, and 1 with multiplicity 3 2 with multiplicity 3, –4 with multiplicity 2, and 1 with multiplicity 4

The given polynomial equation has  roots

–2 with multiplicity 2,

4 with multiplicity 1,

and –1 with multiplicity 3

Given :

A polynomial function

To find out the roots of polynomial function , we set each factor =0 and solve for x

The polynomial function is already in factored form . so we set the factors =0

The exponent of each factor tell us the multiplicity

The given polynomial equation has roots

–2 with multiplicity 2,

4 with multiplicity 1,

and –1 with multiplicity 3

Learn more : link

Take a close look at  f(x )= (x+2)^2 (x+4) (x+1)^3

and notice that the factor x+2 is squared (the root -1 has multiplicity of 2), the factor x+4 is to the first power (the root -4 has multiplicity 1), and the factor (x+1) is cubed (the root -1 has multiplicity 3).  Thus, the first answer choice is the correct one.