Algebra / Geometry III: Unit 1- Polynomial Functions

SUCCESS CRITERIA:

  1. Use the properties of exponents to simplify an expression.
  1. Perform numeric operations to simplify a polynomial expression.
  1. Graph polynomial equations and identify its key features.
  1. Identify roots to a polynomial equation through graphs and factoring.
  1. Write polynomial equations using its zeros.

INSTRUCTOR: Craig ShermanHidden Lake High School

Westminster Public Schools

EMPOWER Recorded TARGETSCALE THEME

MA.11.EE.01.04Polynomial Identities

MA.11.EE.02.04Zeros and Factors of Polynomials

MA.11.EE.03.04Structure of Expressions

PROFICIENCY SCALE:

SCOREREQUIREMENTS

4.0 In addition to exhibiting Score 3.0 performance, in-depth inferences and applications that go BEYOND what was taught in class.

Score 4.0 does not equate to more work but rather a higher level of performance.

3.5 In addition to Score 3.0 performance, in-depth inferences and applications with partial success.

3.0The learner exhibits no major errors or omissions regarding any of the information and processes (simple or complex) that were explicitly taught.

oPerform numeric operations to simplify a polynomial expression, AND

oGraph polynomial equations and identify its key features, AND

oIdentify roots to a polynomial equation through graphs and factoring, AND

oWrite polynomial equations using its zeros.

2.0Can do one or more of the following skills / concepts:

There are no major errors or omissions regarding the simpler details and processes as the learner…

oFactor polynomial expression, OR

oDivide a polynomial expression using synthetic divisionOR

oIdentify key characteristics of a polynomial graph, OR

oFind the zeros(roots) of a polynomial equation by factoring, OR

oWrite a polynomial equation using its roots(zeros).

1.0 Know and use the vocabulary

  • Identify the Basic Elements
  • With help, a partial understanding of some of the simpler details and process

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Factoring Polynomials

INSTRUCTION 1: KHAN ACADEMYINSTRUCTION 2: SOPHIA

INSTRUCTION 3: SOPHIA

When “+c” EXEMPLAR:When “-c” EXEMPLAR:

GIVEN:GIVEN:

STEP 1: Split x2(x )(x )STEP 1: Split x2(x )(x )

STEP 2: Factors of c1* 8 2*4STEP 2: Factors of c1*6 2*3

STEP 3: Factors add to middle term 2 & 4STEP 3: Factors subtract to middle term6 - 1

(x 2)(x 4)(x + 6)(x - 1)

STEP 4: Signs(x + 2)(x + 4)

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Class Work

Factor

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- - - -

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- - - - -

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- - - - -

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Homework

Factor

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- - - -

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- - - -

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Division of Polynomials (Synthetic):

WORD or CONCEPT / DEFINITION or NOTES / EXAMPLE or GRAPHIC REPRESENTATION
Synthetic division

INSTRUCTION 1: KHAN ACADEMYINSTRUCTION 2: SOPHIA

NOTE: means same as (16x5 – 12x3 + 24x2) ÷ (4x2) means same as (16x5 – 12x3 + 24x2) (4x2)-1

EXEMPLAR Divide by a MONomialEXEMPLAR Divide by a BInomial

GIVEN:GIVEN:

STEP 1: Rewrite +-STEP 1: Rewrite 2a4 + 0a3 – 6a2 + 0a - 8

2 0 - 6 0 -8

STEP 2: Reduce a3b + 2a2b – 4aSTEP 2: Coefficients

2 / 2 0 - 6 0 -8

STEP 3:

Class Work

Simplify.

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59The volume a hexagonal prism is and has a height of (t+1) cm. Find the area of the base. (Use V=Bh)

Homework

Simplify.

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  1. The volume a hexagonal prism is (4t3 – 3t2 +7) cm3. The area of the base, B is (t-1) cm2. Find the height of the prism. (Use V=Bh)

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Zeros and Roots of a Polynomial Function:

WORD or CONCEPT / DEFINITION or NOTES / EXAMPLE or GRAPHIC REPRESENTATION
rational root theorem

INSTRUCTION 1: KHAN ACADEMYINSTRUCTION 2: LAMAR

Class Work

How many real zeros does each function below have? Identify any zeros of multiplicity 2 or more. How many imaginary zeros are there?

71..72.73.

Name all of the real and imaginary zeros and state their multiplicity.

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74.

75.

76.

77.

78.

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Homework

How many real zeros does each function below have? Identify any zeros of multiplicity 2 or more. How many imaginary zeros are there?

79.80.81.

Name all of the real and imaginary zeros and state their multiplicity.

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82.

83.

84.

85.

86.

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Zeros and Roots of a Polynomial Function by Factoring:

INSTRUCTION 1: KHAN ACADEMYINSTRUCTION 2:SOPHIA

Class Work

Name all of the real and imaginary zeros and state their multiplicity.

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87. 90.

88. 92.

89. 93.

Homework

Name all of the real and imaginary zeros and state their multiplicity.

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94. 97.

95. 98.

96. 99.

Writing Polynomials from Given Zeros:

INSTRUCTION 1: YOU TUBE

Class work

Write a polynomial function of least degree with integral coefficients that has the given zeros.

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100. 104. 105

101.

102.

103.

Writing Polynomials from Given Zeros: Homework

Name all of the real and imaginary zeros and state their multiplicity.

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106. 109.

107.

108.

110.

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Polynomial Functions UNIT REVIEW

Multiple Choice

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1.

2.A box has volume of and a height of (x+1) cm. Find the area of the base of the box.

  1. (3x + 2) cm2
  2. (3x – 2) cm2
  3. (3x + 5) cm2
  4. (3x – 5) cm2

3.Name all of the real and imaginary zeros and state their multiplicity:

  1. Real zeros: -4 with multiplicity 2; Imaginary zeros: 4i each with multiplicity 1
  2. Real zeros: -4 with multiplicity 3, 4 with multiplicity 1; No imaginary zeros
  3. Real zeros: -4 with multiplicity 4; No imaginary zeros
  4. Real zeros: -4 with multiplicity 2; Imaginary zeros: 2i with multiplicity

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Extended Response

4.A swimming pool is (2x+3) ft by (4x-5) ft.

  1. What area does the pool cover?
  1. A uniform patio of (x+1) ft is to encircle the pool, what area will the patio and the pool occupy?
  1. What is the area of the patio alone?
  1. A fence is needed to go around the patio. How much fence is needed?

5.Graph

  1. Name the real zeros and their multiplicity.
  1. Identify any relative maximums and minimums.

6.The function has a factor of (x – 1).

  1. Reduce f(x) by dividing by (x – 1).

7.Name all of the real and imaginary zeros and state their multiplicity of the function

8.Name all of the real and imaginary zeros and state their multiplicity of the function

9.Write a polynomial function of least degree with integral coefficients that has the given zeros.

-4.5, -1, 0, 1, 4.5,

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