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8 Writing Polynomials and Review_Notes.notebook
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October 29, 2014
Homework in the tray...
Bellwork
1. Is x = 7 a root of f(x) = x2 5x 14 ?
2. Find all roots using the Rational Root Theorem: f(x) = 4x3 12x2 + x 3
5 S
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October 29, 2014
Homework Review
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Table of Contents
Unit 4: Polynomials1. Polynomial Basics 10/202. Graphs of Polynomials 10/213. Products and Factor Theorem 10/224. Long Division 10/235. Synthetic Division 10/24
7. Rational Root Theorem 10/276. Solving Polynomials 10/27
8. Write Polynomials Given the Roots 10/29
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October 29, 2014
Writing Polynomials
Given the Roots 10/29
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October 29, 2014
A quadratic has the solutions x = 3 and x = 2. Find the simplest equation.
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October 29, 2014
Writing Polynomials
Given the Roots 10/29
Complex Conjugate Root Theorem• If P is a polynomial function with realnumber coefficients and a + bi (where b≠0) is a root of P(x)=0, then a – bi is also a root of P(x)=0.
Write a polynomial function, P, in factored form and in standard form by using the given information.
Degree 2
P(0)= 8
Zeros: 2, 5
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October 29, 2014
Write a polynomial function, P, in factored form and in standard form by using the given information.
Degree 3
P(0)= 16
Zeros: 2, 1, 2
8 Writing Polynomials and Review_Notes.notebook
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October 29, 2014
Write a polynomial function, P, in factored form and in standard form by using the given information.
Degree 4
P(0)= 1
Zeros: 1, 3, 2 (multiplicity of 2)
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October 29, 2014
Write a polynomial function, P, in factored form and in standard form by using the given information.
Degree 3
P(0)= 1
Zeros: 1, i
8 Writing Polynomials and Review_Notes.notebook
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October 29, 2014
Write a polynomial function, P, in factored form and in standard form by using the given information.
Degree 4
P(0)= 3
Zeros: 1, 2, 5i
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October 29, 2014
Write a polynomial function in standard form whose zeros are 1, 5i
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ReviewRules:
1.) You can not look back at your group while working a problem out.
2.) You must look me in the eye and say "I'm done," before I say "yes" or "no."
3.) Do not waste time when it is your turn to shoot, or erase.
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October 29, 2014
Name the polynomial by degree and number of terms.
f(x) = x3 + 2x
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October 29, 2014
Name the polynomial by degree and number of terms.
f(x) = 8
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October 29, 2014
Name the polynomial by degree and number of terms.
f(x) = 3x5 + x2 2
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October 29, 2014
Name the polynomial by degree and number of terms.
f(x) = x + 5
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October 29, 2014
Perform the operation.
(8x3 2x2 8x + 7) (4x + 8x2 x3 + 5)
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October 29, 2014
Perform the operation.
(2x3 3)(4x2 5x + 7)
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October 29, 2014
Perform the operation
(x + 3x2 4x4 + 7x3) + (3x x4 4x3)
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October 29, 2014
Perform the operation.
(x+3)(2x 1)(x2 3x + 2)
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October 29, 2014
Divide using long division.
(6x3 + 23x2 + 17x + 6) (3x + 4)
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October 29, 2014
Divide using long division.
(4x4 + x2 + 9x + 4) (2x2 3x + 4)
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October 29, 2014
Divide using synthetic division.
(6x3 + x2 1) (2x 1)
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October 29, 2014
Divide using synthetic division.
(2x3 5x2 + 6x + 4) (x + 2)
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October 29, 2014
Describe the end behavior.
f(x) = x3 2x + 5
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October 29, 2014
Describe the end behavior.
f(x) = 3x4 2x2 + 5
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October 29, 2014
Describe the end behavior.
f(x) = 2x3 + x2 + 4
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October 29, 2014
State the maximum number of turns the graph could make. Then sketch the graph.
Approximate each real zero to the nearest tenth.
Approximate the relative minima and relative maxima to the nearest tenth.
f(x) = x5 3x3 + 2x 2
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October 29, 2014
State the maximum number of turns the graph could make. Then sketch the graph.
Approximate each real zero to the nearest tenth.
Approximate the relative minima and relative maxima to the nearest tenth.
f(x) = x4 + 4x2 3x 5
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October 29, 2014
Find the roots using the rational root theorem!
f(x) = x3 + 64
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October 29, 2014
Find all roots using the Rational Root Theorem
f(x) = 2x3 5x2 x 6
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October 29, 2014
Sketch the graph and state increasing and decreasing intervals.
f(x) = x4 + 4x2 2
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October 29, 2014
Sketch the graph and state the increasing and decreasing intervals.
f(x) = x3 3x2 + 2
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October 29, 2014
Write the polynomial function with:
Degree of 3
Zeros of 3 and 2i
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October 29, 2014
Write the polynomial function with
degree of 4
zeros of 1 , 2, and 2 + i
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October 29, 2014
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