Identify the given roots. Suppose that a graph is presented that crosses the x-axis at -2 and +2; thus the roots of this graph are (x = 2) and (x = -2).
Use algebra to set the two root equations equal to zero. The first root is subtracted by 2 on both sides, and the second root needs 2 added to both sides to have each expression equal zero ((x - 2 = 0) and (x + 2 = 0)).
Multiply the two root expressions using the FOIL method. FOIL is an acronym that describes the steps to multiplying the two expressions---First, Outer, Inner and Last. The first terms of each expression are multiplied and then followed by the two outer terms, the two inner terms and the two last terms.
First: x * x = x^2
Outer: x * 2 = 2x
Inner: -2 * x = -2x
Last: -2 * 2 = -4
Add all of these resulting terms together and combine like terms to identify the polynomial. A polynomial of degree two with roots of -2 and 2 would be (x^2 + 2x + -2x + -4) = (x^2 - 4). Thus, the polynomial is x^2 - 4.