1. A polynomial does not have -intercepts. The graph of a polynomial function has -intercepts.
2. Any given polynomial function can be represented by many different equations, hence your question, properly couched, should have started: "What is an equation..."
3. -intercepts are properly represented by ordered pairs of the form where is a root of the polynomial equation formed by setting the function equal to zero. Plain numbers are not proper representations of -intercepts. You can say that the -coordinate of an -intercept is equal to some number.
So, I will answer the question:
What is an equation of a polynomial function whose graph has the following -intercepts: and ?
If is a root of a polynomial equation in standard form, then is an -intercept of the graph of the polynomial function and is a factor of the polynomial.
For your set of intercepts, the factors of the polynomial are:
Just multiply out the binomial factors to finish the problem.
John
My calculator said it, I believe it, that settles it
