Answer:
[tex]P(x)=x^5 - 12 x^3 + 16 x^2[/tex]
Step-by-step explanation:
P ( x ) has leading coefficient 1
Root of multiplicity n at x= a can be written in factor form (x-a)^n
Roots of multiplicity 2 at x = 2
[tex](x-2)^2[/tex]
Roots of multiplicity 2 at x = 0
[tex](x-0)^2[/tex] is [tex]x^2[/tex]
Roots of multiplicity 1 at x = -4
[tex](x-(-4))^1[/tex] is [tex]x+4[/tex]
multiply all the factors
[tex]P(x)= (x-2)^2 \cdot x^2 \cdot (x+4)[/tex]
[tex]P(x)= x^2(x-2)^2 (x+4)[/tex]
[tex]P(x)= x^2(x^2-4x+4) (x+4)[/tex]
[tex]P(x)=x^5 - 12 x^3 + 16 x^2[/tex]
