1. Pre-Calculus

2.  Step 1: How many complex zeros exist in the above function? 3 OR 6 36

3.  Step 2: Complete the zeros chart. Which chart below is correct? 1?2? Positive RealNegative RealImaginary 201 003 Positive RealNegative RealImaginary 120 102 12

4.  Remember when finding zeros to a polynomial, we look for the term with the highest degree.  Did you add all the degrees together? Remember we only add the degrees together when the polynomial is in factored form. Go back and try to answer again.

5.  Step 3: Find the possible rational zeros using the rational zeros theorem. Which option below is correct? 4, -4, 2, -2, 1, -14, -4, 1, -11, -1, ¼, -¼, -½, ½4, -4, 2, -2, 1, -14, -4, 1, -11, -1, ¼, -¼, -½, ½

6.  To find the positive zeros, you must check the sign change on f(x). You should see one sign change giving one possible positive real zero.  To the find the negative zeros, you must check the sign change on f(-x). You should see 2 sign changes giving one or zero possible negative real zeros.  Remember each row must add to 3 which is the number of zeros you determined in step 1.  Go back and try again.

7. When looking for possible rational zeros, we must use the rational zero theorem.  What are the value for p?  What are the values for q?  What are the value for p/q?  Go back and try again.

8.  Step 4: Use your answers in steps 2 and 3 and use synthetic division to final ALL zeros of the function. You may need to factor or use the quadratic formula to find the final zero(s).  There is a chance of two possible negative zeros so let’s start there. Let’s try -4 using synthetic division.  Did you get zero as a remainder? YESNO

9. Here is what your work should look like using synthetic division with -4.

10. Did you get zero as a remainder? YESNO

11. Here is what your work should look like using synthetic division with -2.

12.  We know we have one negative, based on our chart the other two must be 1 negative and one positive real zero. Let’s solve to find the other zeros.  Can you factor the compressed equation? Or do you need to use quadratic formula? FactorQuadratic Formula

13. Here is what your work should look like using quadratic formula.

14. Final Step: List all zeros of the polynomial function.

15.  The zeros of the function are…