Question

Construct a polynomial function with the following properties: fifth degree, −4 is a zero of multiplicity 4, 2 is the only other zero.

Answer 1

`P(x) =( x+ 4)^(4) (x-2)` is the required polynomial.

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.

⇒
`( x+ 4)^(4)` 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

`P(x) =( x+ 4)^(4) (x-2)`