Presentation on theme: "Homework Log Thurs 11/19 Lesson 5 – 1 Learning Objective:"— Presentation transcript: 1 Homework Log Thurs 11/19 Lesson 5 – 1 Learning Objective: 2 11/19/15 Lesson 5 – 1 Polynomial Functions
3 Learning Objective To classify polynomials 4 Polynomial Degree Name 5 Polynomial # of terms Name 6 Standard Form of a Polynomial Function 7 Write in standard
form & classify by degrees & number of terms
8 End Behavior + 𝑥 𝑒𝑣𝑒𝑛 − 𝑥 𝑒𝑣𝑒𝑛
+ 𝑥 𝑜𝑑𝑑 − 𝑥 𝑜𝑑𝑑 9 11/19/15 Lesson 5 – 2 Polynomials, Linear Factors, & Zeros
10 Learning Objective To analyze the factored form of a polynomial
11 Factor & Find Zeros –15 1. 𝑥 3 −2 𝑥 2 −15𝑥 x 𝑥 2 −2𝑥−15 x 𝑥 2 −5𝑥+3𝑥−15 x(x(x – 5) + 3(x – 5)) x(x + 3)(x – 5) Find zeros by = 0 x(x + 3)(x – 5) = 0 x = 0, –3, 5 –5 3 –2
12 Factor & Find Zeros –12 2. 𝑥 3 − 𝑥 2 −12𝑥 x 𝑥 2 −𝑥−12 x 𝑥 2 −4𝑥+3𝑥−12 x(x(x – 4) + 3(x – 4)) x(x + 3)(x – 4) Find zeros by = 0 x(x + 3)(x – 5) = 0 x = 0, –3, 4 –4 3 –1
13 Write a Polynomial Function From its Zeros
14 (x + 2)(x – 2)(x – 3) = 0 (𝑥 2 −4)(x−3) x – 2 x – 3 x 𝑥 2 –2x 𝑥 2 𝑥 3 15 Write a Polynomial Function From its Zeros 16 Write a Polynomial Function From its Zeros 17 Write a Polynomial Function From its Zeros 18 (x + 2)(x + 2)(x – 2)(x - 3)=0 x 2 x – 3 x 𝑥 2 2x x 𝑥 2 –3x 2 –2 2x
4 19 (𝑥 2
+4x+4) (𝑥 2 −5𝑥+6)=0 -5𝑥 𝑥 2 6 𝑥 2 6 𝑥 2 𝑥 4 -5 𝑥 3 4x 4 𝑥 3 20 Write a Polynomial Function From its
Zeros 21
Multiplicity of a Zero Multiplicity – how many times a factor appears 22 Multiplicity of a Zero 6. What are the zeros of f x = 𝑥(𝑥−3) 4 (𝑥+3) 3 (𝑥+5) 2 ? What are the
multiplicities? x = 0 (multiplicity 1) x = 3 (multiplicity 4) x = –3 (multiplicity 3) x = –5 (multiplicity 2) 23 Multiplicity of a Zero 7. What are the zeros of f x = 𝑥 4 −2 𝑥 3 −8 𝑥 2 ? What are the multiplicities? 𝑓 𝑥 =𝑥 2 ( 𝑥 2 −2𝑥−8) 𝑓 𝑥 =𝑥 2 (𝑥−4)(𝑥+2) Zeros: 𝑥 2 𝑥−4 𝑥+2 =0 x = 0
(multiplicity 2) x = 4 (multiplicity 1) x = –2 (multiplicity 1) 24 Ticket Out the Door Write a cubic polynomial function in standard form with
roots 4, 2, and – 1. 25 Assignment: Pg. 5.1 – 5.2 WS |