Warm-Up: November 16, 2015. Homework Questions? Zeros of Polynomial Functions Section 2.5.

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Presentation transcript:

Warm-Up: November 16, 2015

Homework Questions?

Zeros of Polynomial Functions Section 2.5

Rational Zero Theorem Possible rational zeros = Factors of the constant term Factors of the leading coefficient

Example 1 (like HW #1-8)  List all possible rational zeros for

You-Try #1 (like HW #1-8)  List all possible rational zeros for

Finding Zeros of Polynomial Functions 1. Use the rational zero theorem to find all the possible rational zeros. 2. Use a guess-and-check method and synthetic division to find a zero 3. Use the successful synthetic division to get a lower- degree polynomial that can then be solved to find the remainder of the zeros.

Example 3 (like HW #9-22)  Find all rational zeros of

You-Try #3 (like HW #9-22)  Find all rational zeros of

Example 4 (like HW #9-22)  Solve

You-Try #4 (like HW #9-22)  Solve

Assignment  Read Section 2.5  Page 302 #1-13 odd  An updated 2.5 guided notes has been posted, with a new page 3. It is now 5 pages instead of 4.  You have the rest of class to work on this assignment, or  Chapter 1 Test corrections  Review

First Four Problems  In Exercises 1-8, use the Rational Zero Theorem to list all possible rational zeros for each given function.

Warm-Up: November 17, 2015  Without using your calculator, find all zeros of

Homework Questions?

Linear Factorization Theorem

Example 5 (like HW #23-28)  Factor the polynomial a) as the product of factors that are irreducible over the rational numbers b) as the product of factors that are irreducible over the real numbers c) in completely factored form, including complex (imaginary) numbers

Example 5 (like HW #23-28)  Factor the polynomial

You-Try #5 (like HW #23-28)  Factor the polynomial a) as the product of factors that are irreducible over the rational numbers b) as the product of factors that are irreducible over the real numbers c) in completely factored form, including complex (imaginary) numbers

You-Try #5 (like HW #23-28)  Factor the polynomial

Assignments  Read Section 2.5  Page 302 #1-13 odd,  Page 302 #23-27 odd  Page 302 #29-35 odd, odd (learning next class)  Use your graphing calculator to help find possible roots for odd  You have the rest of class to work on any of the above assignments, Chapter 1 Test corrections, or review.

Warm-Up: November 18/19, 2015  Find all zeros of

Homework Questions?

Finding a Polynomial When Given Zeros

Example 6 (like HW #29-36)

You-Try #6 (like HW #29-36)

Example 7 (like HW #43-56)  Find all roots of

You-Try #7 (like HW #43-56)  Find all zeros of

Assignment  Read Section 2.5  Page 302 #1-13 odd,  Page 302 #23-27 odd  Page 302 #29-35 odd, odd  Use your graphing calculator to help find possible roots for odd