1. 6.6: FINDING RATIONAL ZEROS Objectives: Students will be able to… Find all real zeros of a polynomial function Use the rational zero test to determine any rational zeros of a polynomial

2. Rational Zeros If a polynomial has integer coefficients, then every rational zero has the form: factor of constant term____ factor of leading coefficient

3. Rational Zeros…  You can make a list of all rational zeros by listing all factors of constant term over factors of the leading coefficient List all possible rational zeros for

4. How do you suppose we would figure out which one of these possible zeros is in fact a zero???  Divide using synthetic division. If the remainder is 0, then it’s a 0.  If the remainder = 0, then f( )= 0

5. Find all real zeros of f(x) = x 3 – 4x 2 -11x +30 1. List all possible rational zeros: 2. Test values using synthetic division. If the remainder is 0, then it is a 0. 3. Set quotient = 0 and solve. (May need to repeat step 2 to get a polynomial that can be solved algebraically)

6. Find all real zeros of f(x) = 15x 4 – 68x 3 -7x 2 +24x -4

7. Find the rational zeros: 1. f(x) = x 3 – x 2 -9x +92. f(x)=x 3 – 7x 2 +10x +6

8. Application Problem: A rectangular column of cement is to have a volume of 20.25 ft 3. The base is to be square, with sides 3 ft less than half the height of the column. What should the dimensions be?

9. Application Problem: A company that makes salsa wants to change the size of its cylindrical salsa cans. The radius of the new can will be 5 cm less than the height. The container will hold 144 cm 3 of salsa. What are the dimensions of the new container?