TEKS: 2A.10F. Terms. Functions Equations Inequalities Linear Domain Factor

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1 POLYNOMIALS UNIT TEKS: A.10F Terms: Functions Equations Inequalities Linear Domain Factor Polynomials Monomial, Like Terms, binomials, leading coefficient, degree of polynomial, standard form, terms, Parent Function, trinomials, distribute, Synthetic division, Simplify Solution Essential Questions: How do we determine domain restrictions? Formulate a rational equation or inequality using linear or quadratic functions to model a situation Solve rational equations and inequalities using algebraic techniques Describe the process for simplifying a rational epression Learning Outcomes: Determine domain restrictions Solve equations and inequalities algebraically Identify rational epressions from various representations Determine reasonable domain and range Determine solutions using algebraic methods Topic Objective Teacher Lesson Introduction & monomial number, variable or the product of numbers and variables degree of a monomial sum of the eponents of the variables Vocabulary E: Find the degree of each monomial 1. -a b 4 Degree: 6. 4 Degree: y Degree: 1 polynomial monomial or the sum or difference of monomials degree of a polynomial - determined by the monomial with the highest degree E: Find the degree of each polynomial Degree: 5..5 y +.5y +.75 Degree: Degree: 4 Eponent, Rational eponent, Base standard form of a polynomial written with terms in order from greatest to least (highest to lowest power) leading coefficient the coefficient of the first term E: Write each polynomial in standard form, then give the leading coefficient Leading Polynomial Standard Form Coefficient y 3 + y 5 + 4y y 5 + y 3 + 4y 1 Some polynomials have special names based on their degree and the number of terms they have. Degree Name Terms Name 0 Constant 1 Monomial 1 Linear Binomial Quadratic 3 Trinomial 3 Cubic 4+ Polynomial 4 Quartic 5 Quintic 6+ 6 th degree, etc.

2 Addition & Subtraction Can I add & subtract E1: ( + 1) + (3 4 6) E: ( ) (3 + 4) Multiply Polynomials Can I multiply Use a Kuts WS or Pizzaz puzzle to review. Warm-up: Put the following problems on the board and check answers: 1. 3 ( + ) ( 1)( + ) + 3. (3 + 5) ( 7) + 1 How do you know which operation to perform? What is the difference between problem & 3? What method do I use for problem? What method do I use for problem 3? Why? How do I know which method to use? Put subtraction of two trinomials on the board. Ask the questions. Point out that someone will try to multiply them on the test. E. ( + )( + 4 3) E: ( + 1)( 5 + 7) OYO: ( 3)( + 5 1) E: ( + 4)( + 3) E. ( ) 3 OYO: ( + 6) 3 write epanded first E: Find the surface area of a rectangular prism with sides of,, and +1. SA = ( )( ) + 4( )( + 1) SA = ASGN: p.418 #19-7, 9 Figure out Pascal s Triangle. E1: ( + ) E: ( + ) Long Division Can I divide 3 4 (4 5) (3 + 1) E3: E4: Warm-up: Work / 1 on the board. Write down the steps. What are the steps? What is the number left at the bottom? Remainder What does that mean? What if the remainder is 0? What does it mean? Remember eponent rules? What do I do to eponents if multiplying? What do I do to eponents if dividing? Use the same steps to work eamples. See printed notes & slide #3.

3 E: ( ) ( + ) E: E: ( ) ( 4) E: Synthetic Division Can I divide ASGN: p.46 #13-18 or #39-48 Warm-up: Do you want an easier way to work the problems from yesterday? Show slide #4. Work same eamples from day before using synthetic division method. Put one problem worked both ways side by side. What are the steps for synthetic division? Compare the two methods. What do you see that is the same? What do you see that is different? What is the last number? What does it mean? What if the remainder is 0? What does it mean? How do you know the eponents of the answer? *The coefficient of in the divisor must equal 1 to use this method. E: ( ) ( + ) E: 4 ( ) ( +5) Factor *E: (3 + 8 ) (3 1) *E: ASGN: p.46 #19-4 0r #39-48 : (-a) is a factor if P(a)=0. Application: Calculate P(a). Does it equal zero? Eamples ( ) (3 + 1)

4 Remainder ASGN: p.46 #1-31odd, 49, 50, 51 : If P() is divided by (-a) and the remainder is zero, then a is a root. If the remainder is not equal to zero, then P(a) is a root. Application: Use synthetic division. Is the remainder zero? If not, calculate P(a). That is a root. p.433 #-8 even Rational Root ASGN: p.433 #1-39 odd, 53 : If the polynomial P() has integer coefficients, then every root of the equation can be written in the form p/q. Where p is a factor of the constant and q is a factor of the leading coefficient. Application: Find all of the factors of p & q. Combine them as p/q and use synthetic division to determine if it is a root. Graphing End Behaviors ASGN: p.44 #-7, 4-6, Even eponents the ends face the same direction. Leading coefficient: (+) = up, (-) = down Odd eponents the ends face opposite directions. Leading coefficient: (+) = left-down, right-up; (-) = left-up, right-down,

5 Review Work Review Sheet. Have eamples clipped on board for students to use during the review.