Roots, Factors, and the Polynomial Function
- Mark Beckwith
Use the New Function f(x) button to generate a new polynomial function. Zoom and change the window to find an appropriate view of the function in order to determine the roots of the function.
1) From the graph of the polynomial function, you should be able to determine its integer roots. Use the Properties of f(x) button to display the function's properties. After you determine the function's integer roots, check your answers with the Roots of f(x) checkbox.
2) Knowing the integer roots of f(x), you can determine the possible factors of f(x). Check your answers with the Possible Factors of f(x) checkbox.
3) With the possible factors of f(x) and based on the behavior of the graph near its roots, you can determine the degree of each factor of f(x). Write f(x) as a polynomial function in factored form. Check your answer with the f(x) in Factored Form checkbox.
4) By multiplying the factors of f(x), you can write f(x) as a polynomial function in standard form. Completely multiply all factors of f(x) and check your answer with the f(x) in Standard Form checkbox.