Find a polynomial function of degree 5 with -1 as a zero of multiplicity 3,0 as a zero of multiplicity 1 , and 1 as a zero of multiplicity 1. The polynomial function in expanded form is $\mathrm{f}(\mathrm{x})=\square$. (Use 1 for the leading coefficient.)

Step 1 ：The problem is asking for a polynomial function of degree 5 with given zeros and their multiplicities. The zeros are -1 with multiplicity 3, 0 with multiplicity 1, and 1 with multiplicity 1.

Step 2 ：A polynomial function with given zeros can be found by multiplying factors of the form \((x - a)\) for each zero a. The multiplicity of a zero is the number of times the factor \((x - a)\) appears in the polynomial.

Step 3 ：For this problem, the polynomial function can be found by multiplying the factors \((x - (-1))\), \((x - 0)\), and \((x - 1)\) with their respective multiplicities.

Step 4 ：The factor \((x - (-1)) = (x + 1)\) should appear 3 times because -1 is a zero of multiplicity 3. The factor \((x - 0) = x\) should appear 1 time because 0 is a zero of multiplicity 1. The factor \((x - 1)\) should appear 1 time because 1 is a zero of multiplicity 1.

Step 5 ：So, the polynomial function is \(f(x) = (x + 1)^3 * x * (x - 1)\).

Step 6 ：After expanding this polynomial function, we get \(f(x) = x^5 + 2x^4 - 2x^2 - x\).

Step 7 ：This is the polynomial function of degree 5 with -1 as a zero of multiplicity 3, 0 as a zero of multiplicity 1, and 1 as a zero of multiplicity 1.

Step 8 ：Final Answer: The polynomial function in expanded form is \(\boxed{f(x) = x^5 + 2x^4 - 2x^2 - x}\).