Question

Find a polynomial function with leading coefficient 1 that has the given zeros, multiplicities, and degree.

Zero: 3, multiplicity: 1
Zero: 2, multiplicity: 3
Degree: 4

Zero: 3, multiplicity: 3
Zero: 0, multiplicity: 2
Degree: 5

Answer 1

We are to find a polynomial function with leading coefficient 1 that has:

4 degrees; 3 zeros; 1 multiplicity

To have 4 degrees the function's variable should have 4 as the highest power. It should also have 3 factors equivalent to 3 zeros.

Example:

f(x) = x^4 - 2x^3 + 4x^2 - x + 1