Identify how many zeros, or roots, the graph contains and make sure it corresponds to the highest ordered polynomial in the equation. This is done by entering the polynomial expression into the "y=" section of the graphing calculator and graphing the polynomial. For example, a polynomial of degree 3, meaning the highest exponent in the polynomial is a 3, will have 3 areas on the graph where it intersects the x-axis.
The roots can be identified by pressing "Math," then "Zero" to identify the upper and lower bound for a particular intercept. These bounds can be any value on the x-axis that serve as an upper and lower limit for the particular intercept. For example, if the graph appears to cross the x-axis at 2, then -1 and 4 would be reasonable lower and upper bounds respectively, as the root falls between these two values. This process should be repeated for each root on the graph.
Copy down the roots in the form of x=corresponding root value. For example, if second degree polynomial has roots of -4 and 2, they should be written as: x = -4 and x = 2
To put the roots in the correct factored form, solve for each expression to equal zero and place the two individual expressions side-by-side for the final factored form. Using the previous example, a second degree polynomial with roots of -4 and 2 would be written as:
(x+4 )(x-2).
x + 4 = 0 and x -- 2 = 0
(x+4)(x-2)
These two expressions can be multiplied together, using the FOIL method, to check the answer. The product of these two expressions should equal the original polynomial graphed by the calculator. Instructions for performing the FOIL method are provided in the Resources section.
It should be noted that most math instructors will want to see these types of problems factored by hand instead of using this shortcut with a calculator. Nevertheless, this method is an excellent way to check an answer if a problem has been factored by hand.