Find a polynomial function with the following characteristics: Degree of 4; zero of 2, multiplicity 2, zero of 1, multiplicity 2, and the graph of the function falls to the left and right.

Answer 1

Use thr factored form of a polynomial:

f(x) = a(x-p)(x-q)(x-r)(x-s)....

1. a = a constant
2. p, q, r, s, etc are the zeros

Degree of 4: means you need four factors

zero of 2, multiplicity 2: (x-2)(x-2) = (x-2)²

zero of 1, multiplicity 2: (x-1)(x-1) = (x-1)²

the graph of the function falls to the left and right: a = -1

f(x) = -(x-2)²(x-1)²