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Ch6 Polynomials and Polynomial Functions Cross-Curricular Ties: I Can… F.IF.4-9 Identify the number of turns and model a situation using different degree polynomials. A.SSE.1 Interpret parts of an expression, such as terms, factors, and coefficients A.APR.2 Know and apply the Remainder Theorem A.APR.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial Rewrite simple rational expressions in different forms A.APR.6 A.APR.1 (2) A.SSE.2(2) N.CN.8 * N.CN.9* A.APR.5* Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Use the structure of an expression to identify ways to rewrite polynomials. Keywords: Imaginary number -complex number (form) -Conjugate (Complex) -Relative Maximum and Minimum -Zeros -Roots -Multiplicity of Polynomial -Synthetic Division -Remainder Theorem -Sum and Difference of Cubes -Rational Root Theorem -Fundamental Theorem of Algebra Extend polynomial identities to the complex numbers Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials Use Pascal’s Triangle to expand a binomial Project ties: Topic(s) Suggested Text PH2011 Common Core End Behavior, graphing polynomials Pg 306 ext 6.2 F.IF.4-9, A.SSE.1, A.APR.2, A.APR.3 Dividing polynomials 6.3 A.APR.6 Science, Technology, Engineering, & Math (STEM) Activities Solving Polynomial Equations 6.4 A.APR.1, A.SSE.2A.APR. 3 Models 6.4 A.APR.1, A.SSE.2 Polynomial Function Theorems 6.5/6.6 *N.CN.8( ex 4 and 5) N.CN.9* A.APR.2 Pascal’s Triangle, expanding a binomial 6.8/Review A.APR.5* Always a good review of all functions Step 1 2 3 4 5 6 7 8 9 10 11 Activity Make a set of 3x5 index cards for each keyword. Imaginary numbers prank youtube Pg 274 example 1 Kahn academy simplifying negative roots, and 2 What is a complex number kahn Pg 278 1-17 odd Adding Complex Numbers, Examples 5, 6, and 7 in book Multiplying Complex Numbers, pg 276 - 277 and Using quadratic for imaginary solutions Pg 278 29-45 odd, 50-53 Use 3x5 cards and do pg 306 Technology Activity. Write your answers for 1-4 on a separate sheet of paper. If there are questions on how to do this please ask. Review the classifying Classifying Review polynomials notes polynomials Book Powerpoint video on classifying Take the quiz here, and check your answers. Do pg 309 1-12. PowerPoint on polynomial Steps for fitting regressions to fitting the calculator 1. Pick two data sets from here. Find one you think is linear and one you think is a polynomial relation. 2. Give the equation for their function of best fit using the Mastery 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 calculator. 3. How closely do they fit this function? How do you know this? Read the extension on end behavior on pg 312 Do pg 312 1-9 odd Watch the kahn academy here, and look at example 1 on page 313. Watch the video on finding the Read example 2 GCF at kahn Copy the picture showing relative maximum, minimum and x intercepts at the top of pg 315 into your Know it all Books. Review example 4-6 on page 315-316, write down the equivalent statements in the Key concepts box at the bottom of page 316 into your know it all books. A very important tool/cheat to use on a graphing calculator Do page 317 1-35 odd. Mastery Test on F.IF.4-9 Watch dividing Look at examples 1, on Watch the polynomials on kahn page 321 video on achademy dividing polynomials at here Look at example 2 on pg 321 Pg 324 9-12 Doing Synthetic Division 1, 2, Look at examples 3 and 5 on Dr. Bob doing Synthetic pg 322 and 323 respectively. Evaluation. Copy down example 5 on page 323 into your Know it all Book. What would you get as a remainder if you evaluated the function at a root? Do pg 324 13 – 21 odd, 27 – 35 odd Pg 327 Example 1 Regents notes 1, 2 practice Write down all problems on a separate sheet, do pg 330 1-5 odd Factor the following difference Examples 3, 4, and 5 of cubes kahn 1, 2, factoring special products Pg 330 15-31 odd Using the rational A peaceful Example 1 and 2, on root theorem to video on page 336 find solutions rational roots Pg 339 1-12 all Complex zeros theorem, Example 3, 4,5 Optional X 34 35 36 37 38 irrational root theorem Pg 339 1-31 odd Fundemental theorem 1, 2 Example 1, 2 Pg 343 1-25 odd Review Pick one problem from each set of problems pg 301 39 – 50, 55-58, pg 359 6-51 Test http://phschool.com/webcodes10/index.cfm?area=view&wcprefix=auk&wcsuffix=0099 Chapter PowerPoints http://www.taosschools.org/ths/Departments/MathDept/quintana/GeometryPPTs/index.htm