Pre-Calculus Assignment Sheet Unit 8-3rd term January 20 th to February 6 th 2015 Polynomials

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1 Pre-Calculus Assignment Sheet Unit 8- rd term January 0 th to February 6 th 01 Polynomials Date Topic Assignment Calculator Did it Tuesday Multiplicity of zeroes of 1/0/1 a function TI-nspire activity TI-nspire activity Wednesday 1/1/1 Factoring polynomials Notes pages and Tetbook p. A A #s every other odd Verify Factoring Thursday 1//1 Factoring polynomials Tetbook p. A #s Multiples of Verify Factoring Friday 1//1 Monday 1/6/1. Polynomial Functions of a Higher Degree Notes pages and. Continued Factoring Quiz Tetbook pp #s 1 8 all, 9 1 odd, 7 7 odd, 7 9 odd Tetbook pp #s 10, 1 even, 8 8 even, 8 60 even Verify answeres Tuesday 1/7/1. Polynomial and Synthetic Division Notes page 6 Tetbook pp #s 9 odd, 19 7 odd,,, 9 6 odd, 7, 77, 8 Wednesday 1/8/1. Continued Quiz on. Tetbook pp #s 6 1 even, 0 0 even, 6, 0 6 even, 76, 8 Thursday 1/9/1. Comple Numbers Notes page 7 Tetbook pp #s 1 1 odd, 17 odd, 7 1 odd, 7, 1,, 7, odd, 7 81 odd Friday 1/0/1. Continued Quiz on. Tetbook pp #s, 6 1 even, 18, 0,, 8, 0,, 8, 0, 6, 8, 0, even, 76 8 even Monday //1. Zeros of Polynomials Notes pages 8 and 9 Tetbook pp #s, 7, 11, 1, 1, 7, 7,, 7, 9, 1, 9, 6, 69, odd Tuesday //1. Continued Quiz on. Tetbook pp #s 8 16 even,, 6, 8,, 8, 0, 6, 66, even Wednesday //1. Continued Worksheet- handout Thursday //1 Review Quiz on. Study for test Friday /6/1 Test #8 Print out Unit 9 assignment sheet 1

2 January 1, 01 Polynomials and Factoring a n a a A polynomial in is an epression of the form: n n 1 0 where a 0 n a 0 n is the degree of the polynomial a n is the leading coefficient a 0 is the constant term 1 st rule of factoring is take out the Greatest Common Factor, the GCF: nd Look for one of the following factoring types: rd How can you use the calculator to verify? Difference of Squares a b Eample 1: 9 16 ( a b)( a b) Eample : 16m 100m Sum of Squares Eample 1: 9 Eample : a b ( a bi)( a bi) m 7m Difference of Cubes Eample 1: 8 7 Eample : 7m 1000 a b ( a b)( a ab b ) Sum of Cubes Eample 1: 0 Eample : a b ( a b)( a ab b ) 0n 18n Perfect Square Trinomials E 1: 16 9 E : a ab b or a ab b ( a b) ( a b)

3 Factoring a Trinomial with a leading Coefficient of 1. b c and b c Factors of c that add up to b or b Eample 1: 7 6 Eample : 7 6 b c and b c Factors of c that subtract to b or b Eample 1: 6 Eample : 6 Factoring a Trinomial with a leading Coefficient of NOT 1. a b c a b c a b c a b c use factor chart of ac E 1: 1 E : 1 6 E : n 61n E : 1 Factoring by Grouping Given terms ***(or more) step one: group the terms into two pairs ***(if needed) step two: take out the GCF of each pair step three: if the remaining binomials match, then factor out the binomial ***(simplify terms that are left) E 1: 6 E : 6 8 ***E : ( 1)( ) ( 1) ( )

4 January, 01. Polynomial Functions of a Higher Degree a n a n a a Polynomial function : n n 1 0 To describe the end behavior (right-hand and left-hand behavior) of a polynomial, look at the leading coefficient and the degree of the polynomial Even degree polynomial Sketch Describe Odd degree polynomial Sketch Describe Positive leading coefficient Rises to the Left Rises to the Right Negative leading coefficient Rises to the Left Falls to the Right Shape of graph: Roots/Zeros all different or Repeating Roots/Zeroes (Multiplicity of k) Degree 1 Normal shape Description (end behavior, turning points, etc.) Repeating roots/zeros Description (end behavior, turning points, etc.) 1.) Given: p ( ) ( )( )( 1) ( ) Find: a) the degree: b) the real zeros with multiplicity: c) the y- intercept: d) Describe the end behavior. e) number of turning points:

5 .) Given: p ( ) ( 1) ( ) ( ) Find: a) the degree: b) the real zeros with multiplicity: c) the y- intercept: c) Describe the end behavior. e) sketch.) Given: p ( ) (1 )( ) Find: a) the degree: b) the real zeros with multiplicity: c) the y- intercept: c) Describe the end behavior. e) sketch.) Given: f ( ) 6 Find: a) the degree: b) the real zeros with multiplicity: c) the y- intercept: c) Describe the end behavior. e) sketch Write an equation with the given zeros:.) -, 0, 1, 6.) - degree is 7.)

6 January 7, 01. Polynomial and Synthetic Division, Remainder and Factor Theorems 1. Divide using Long Division:. Divide using Synthetic Division:. Divide: ) ( ) ) ( ) Use synthetic division to find each function value. Use the calculator to verify g ( ) 6 Find: g ( ) and g1. Use synthetic division to show that is a solution, then factor the polynomial completely = 6. Verify the factors of the given function, then find the remaining factors. list all the real zeros of the function and confirm by using your calculator. f ( ) Factors: ( ) and ( + ) 6

7 January 9, 01. Comple Numbers i 1 if a term has an i it is called i 1 imaginary Comple Number: Real # + Imaginary # i i i 1 Standard Form: a + bi where a is the real part and bi is the imaginary part Addition and Subtraction of Comple Numbers: combine like parts E: i ( -i + i ) ( + i ) +7 Conjugates: a + bi and a bi Multiply to a Real number, always come in pairs as roots to a polynomial. E: Multiply 8i and 8i Simplify. Write answer in Standard Form i i. i i i. ( 6i 7) ( i). 1 i 6. ( i)( i) 7. ( 6i)( 7i) 8. i 9. 6 i i 10. i 1 i i Solve usingthe Quadratic Formula: b b ac a 7

8 February, 01. Zeros of Polynomials The Rational Root Theorem Given a polynomial: The only Possible Rational Roots can be found by dividing the factors of the Constant by the factors of the Leading Coefficient. n n1 Rational Zero Test: If the polynomial f ( ) an an 1... a1 a0 has integer coefficients, every rational zero of f has the form Rational zero = q p where p and q have no common factors other than 1 and where p = a factor of the constant and q = a factor of the leading coefficient E: List all the possible Rational Roots of : DesCartes Rule of signs: The number of positive roots is the number of sign variations in a polynomial f (). The number of negative roots is the number of sign variations in a polynomial f ( ). We will use a PNI ( positive, negative, imaginary) chart. Find all the rational Zeros. 1 st List all the possible roots. nd Determine a PNI chart. rd Solve the given polynomial using synthetic division. th Write in factored form. 1. f ( ) p ( )

9 Find all the rational Zeros. 1 st List all the possible roots. nd Determine a PNI chart. rd Solve the given polynomial using synthetic division. th Write in factored form ) ( p. 1 1 ) ( f Use the given Zero to find all the zeros of the function.. ) ( f Zero: i ) ( f zero: i 9