Question

Find a polynomial function of degree 5 with -2 as a zero of multiplicity 3,0 as a zero of multiplicity 1, and 2 as a zero of multiplicity 1.

Answer 1

Answer:
`f(x)=x^5+4x^4-16x^2-16x`Step-by-step explanation:

The zeros and their multiplicities are:

-2 with multiplicity 3

0 with multiplicity 1

2 with multiplicity 1

The polynomial function is therefore given as:

`\begin{gathered} f(x)=(x+2)^3(x-0)^1(x-2)^1 \\ f(x)=x(x-2)(x+2)^3 \\ f(x)=(x^2-2x)(x^3+6x^2+12x+8) \\ f(x)=x^5+6x^4+12x^3+8x^2-2x^4-12x^3-24x^2-16x \\ f(x)=x^5+4x^4-16x^2-16x \end{gathered}`

Therefore, the polynomial function of degree 5 is:

`f(x)=x^5+4x^4-16x^2-16x`