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.
The given polynomial equation has roots
–2 with multiplicity 2,
4 with multiplicity 1,
and –1 with multiplicity 3
Given :
A polynomial function [tex]f(x)= (x+2)^2(x+4)(x+1)^3[/tex]
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
[tex](x+2)^2 (multiplicity =2)\\ (x+2)^2=0\\x+2=0\\x=-2[/tex]
[tex](x+4)=0\\x=-4 (multiplicity =1)[/tex]
[tex](x+1)^3 (multiplicity =3)\\x+1=0\\x=-1[/tex]
The given polynomial equation has roots
–2 with multiplicity 2,
4 with multiplicity 1,
and –1 with multiplicity 3
Learn more : brainly.com/question/11311587
