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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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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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Writing Polynomials
Given the Roots 10/29
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A quadratic has the solutions x = 3 and x = 2. Find the simplest equation.
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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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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
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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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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
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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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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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Name the polynomial by degree and number of terms.
f(x) = x3 + 2x
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Name the polynomial by degree and number of terms.
f(x) = 8
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Name the polynomial by degree and number of terms.
f(x) = 3x5 + x2 2
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Name the polynomial by degree and number of terms.
f(x) = x + 5
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Perform the operation.
(8x3 2x2 8x + 7) (4x + 8x2 x3 + 5)
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Perform the operation.
(2x3 3)(4x2 5x + 7)
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Perform the operation
(x + 3x2 4x4 + 7x3) + (3x x4 4x3)
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Perform the operation.
(x+3)(2x 1)(x2 3x + 2)
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Divide using long division.
(6x3 + 23x2 + 17x + 6) (3x + 4)
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Divide using long division.
(4x4 + x2 + 9x + 4) (2x2 3x + 4)
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Divide using synthetic division.
(6x3 + x2 1) (2x 1)
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Divide using synthetic division.
(2x3 5x2 + 6x + 4) (x + 2)
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Describe the end behavior.
f(x) = x3 2x + 5
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Describe the end behavior.
f(x) = 3x4 2x2 + 5
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Describe the end behavior.
f(x) = 2x3 + x2 + 4
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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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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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Find the roots using the rational root theorem!
f(x) = x3 + 64
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Find all roots using the Rational Root Theorem
f(x) = 2x3 5x2 x 6
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Sketch the graph and state increasing and decreasing intervals.
f(x) = x4 + 4x2 2
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Sketch the graph and state the increasing and decreasing intervals.
f(x) = x3 3x2 + 2
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Write the polynomial function with:
Degree of 3
Zeros of 3 and 2i
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Write the polynomial function with
degree of 4
zeros of 1 , 2, and 2 + i
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