Analyzing a polynomial...

Make and analyze a polynomial function using the ideas you have learned throughout this unit (unit 1: polynomial functions).

1. make a function made up of the product of at least three binomials. However..;

• At least one of the binomials must be of the form (ax + b) where a1
• Your function must contain an x-intercept of order 2.

2. Expand and simplify your function into standard form (using the function you've created).

3. Demonstrate how you can prove that one of the binomials you wrote inquestion 1 is a factor of the function you have written in standard form.

4. Apply one of the factoring processes shown in this unit to fully factor your polynomial in order to prove that it is made up of the product of binomials from question 1 (could be factor theorem?). Be sure to state the x-intercepts and y-intercept of your function.

5. Apply the information you have gathered about your function to draw an accurate graph of your function. Describe the end behaviour of your function (describe the end behaviour and draw it... such as x approaches -infinity...).