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Homework Log
Thurs
11/19
Lesson 5 – 1
Learning Objective: To classify polynomials
Hw: 5.1 – 5.2 WS
11/19/15 Lesson 5 – 1 Polynomial Functions
Algebra II
To classify polynomials
Learning Objective
5
x + 4
Polynomial DegreeName
0
1
2
3
4
5
Constant
Linear
Quadratic
Cubic
Quartic
Quintic
5
x + 4
Polynomial # of terms Name
1
2
1
3
2
4
Monomial
Binomial
Monomial
Trinomial
Binomial
Polynomial
Arrange the terms by degree in descending numerical order.
Write in standard form & classify by degrees & number of terms.
1. Quadratic Trinomial
Standard Form of a Polynomial Function
2. Quartic Polynomial
3.
Quintic Binomial
Write in standard form & classify by degrees & number of terms
End Behavior
11/19/15 Lesson 5 – 2 Polynomials, Linear
Factors, & ZerosAlgebra II
To analyze the factored form of a polynomial
To write a polynomial function from its zeros
Learning Objective
1. x(x(x – 5) + 3(x – 5)) x(x + 3)(x – 5)Find zeros by = 0 x(x + 3)(x – 5) = 0x = 0, –3, 5
Factor & Find Zeros –15
–23–5
2. x(x(x – 4) + 3(x – 4)) x(x + 3)(x – 4)Find zeros by = 0 x(x + 3)(x – 5) = 0x = 0, –3, 4
Factor & Find Zeros –12
–13–4
3. What is a cubic polynomial function in standard form with zeros –2, 2, and 3?x = –2 x = 2 x = 3x + 2 = 0 x – 2 = 0 x – 3 = 0(x + 2)(x – 2)(x – 3) = 0
Write a Polynomial Function From its Zeros
(x + 2)(x – 2)(x – 3) = 0
– 2 x
–2x 𝑥2
–42x
x
2
– 3 x
–3 𝑥3
12–4x
–4
3. What is a cubic polynomial function in standard form with zeros –2, 2, and 3?x = –2 x = 2 x = 3x + 2 = 0 x – 2 = 0 x – 3 = 0(x + 2)(x – 2)(x – 3) = 0
Write a Polynomial Function From its Zeros
4. What is a cubic polynomial function in standard form with zeros 0, 5, and 5?x = 0 x = 5 x = 5x = 0 x – 5 = 0 x – 5 = 0(x)(x – 5)(x – 5) = 0
Write a Polynomial Function From its Zeros
5. What is a quartic polynomial function in standard form with zeros –2, –2, 2 and 3?x = –2 x = –2 x = 2 x = 3x+2=0 x+2=0 x–2=0 x-3=0(x + 2)(x + 2)(x – 2)(x - 3)=0
Write a Polynomial Function From its Zeros
(x + 2)(x + 2)(x – 2)(x - 3)=0
2 x
2x 𝑥2
42x
x
2
– 3 x
–3x𝑥2
6–2x
x
–2
(𝑥¿¿2−5 𝑥+6)¿
=0
-5 𝑥4
–204
4x
-5 𝑥2 6
6
24x
4 -20x 24 4
𝑥4−𝑥3−10 𝑥2+4 𝑥+24=0
5. What is a quartic polynomial function in standard form with zeros –2, –2, 2 and 3?x = –2 x = –2 x = 2 x = 3x+2=0 x+2=0 x–2=0 x-3=0(x + 2)(x + 2)(x – 2)(x - 3)=0
Write a Polynomial Function From its Zeros
Multiplicity – how many times a factor appears
Even multiplicity – TOUCHES the x-axis, will NOT cross
Odd multiplicity – CROSSES the x-axis
Multiplicity of a Zero
6. What are the zeros of ? What are the multiplicities?
x = 0 (multiplicity 1)x = 3 (multiplicity 4)x = –3 (multiplicity 3)x = –5 (multiplicity 2)
Multiplicity of a Zero
7. What are the zeros of ? What are the multiplicities?
Zeros: x = 0 (multiplicity 2)x = 4 (multiplicity 1)
x = –2 (multiplicity 1)
Multiplicity of a Zero
Write a cubic polynomial function in standard form with roots 4, 2, and – 1.
Ticket Out the Door
Assignment:
Pg. 5.1 – 5.2 WS
