Find a polynomial f(x) with leading coefficient 1 and having the given degree and zeros.

Question

degree 4;    zeros −2, ±1, 4

f(x) =

Answer 1

First, recognize that there is a factor for each solution (the "zeros"). So the factors are:

x + 2

x + 1 and x - 1, which is the same as x^2 - 1

x - 4

Multiply all these together, and you'll have a 4th-degree polynomial.. Adjust the coefficients as required for the leading coefficient to be equal to 1.