Answer:
[tex]P(x) =( x+ 4)^{4} (x-2)[/tex] is the required polynomial.
Step-by-step explanation:
Multiplicity of the polynomial = 5
⇒The highest power of the variable in the polynomial is 5.
Now, the zero of the polynomial is -4 with multiplicity 4.
⇒[tex]( x+ 4)^{4}[/tex] is one the factor of the polynomial.
Also, the only other zero of the polynomial is 2 with multiplicity 1.
⇒(x-2) is the ONLY other factor of the polynomial.
Hence, the required polynomial P(x) is
[tex]P(x) =( x+ 4)^{4} (x-2)[/tex]
