6­2 Day 2 Polynomials and Linear Factors 2011
January 12, 2011
6­2 Day 2 Polynomials and Linear Factors
Objective
Write a polynomial function from its zeros.
Jan 3­12:26 PM
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6­2 Day 2 Polynomials and Linear Factors 2011
January 12, 2011
Review:
1. Write this polynomial in standard form: ﴾x + 1﴿﴾x ­ 2﴿﴾x+3﴿
2. Write this polynomial in factored form: x3 ­ x2 ­12x
Jan 3­12:33 PM
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6­2 Day 2 Polynomials and Linear Factors 2011
January 12, 2011
What are ZEROS of a graph?
ZEROS are:
x­intercepts ﴾where the graph crosses the x­axis﴿
roots
solutions
Jan 3­12:37 PM
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6­2 Day 2 Polynomials and Linear Factors 2011
January 12, 2011
Find the zeros of y = ﴾x ­ 2﴿﴾x + 1﴿﴾x + 3﴿
Using the Zero Product Property, find a zero for each linear factor:
x ­ 2 = 0
x = or
x + 1 = 0
x = or
x + 3 = 0
x = Jan 3­12:49 PM
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6­2 Day 2 Polynomials and Linear Factors 2011
January 12, 2011
Find the zeros of y = ﴾x ­ 7﴿﴾x ­ 5﴿﴾x ­ 3﴿
Jan 3­12:53 PM
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6­2 Day 2 Polynomials and Linear Factors 2011
January 12, 2011
You can reverse this process and write linear factors when you know the zeros!
Jan 3­12:54 PM
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6­2 Day 2 Polynomials and Linear Factors 2011
January 12, 2011
Write a polynomial function in standard form
with zeros at ­2, 3, and 3.
Jan 3­12:56 PM
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6­2 Day 2 Polynomials and Linear Factors 2011
January 12, 2011
Write a polynomial function in standard form
with zeros at ­4, ­2, and 0.
Jan 3­12:59 PM
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6­2 Day 2 Polynomials and Linear Factors 2011
January 12, 2011
f﴾x﴿ = ﴾x + 2﴿﴾x ­ 3﴿﴾x ­ 3﴿
If a polynomial function has a zero that is repeated, it is called a MULTIPLE ZERO.
In the function above, the number 3 is a multiple zero.
A multiple zero has MULTIPLICITY equal to the number of times the zero occurs.
In the function above, the zero 3 has multiplicity 2.
Jan 3­1:01 PM
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6­2 Day 2 Polynomials and Linear Factors 2011
January 12, 2011
Find any multiple zeros of f﴾x﴿ = x4 + 6x3 + 8x2 and state the multiplicity.
0 is a multiple zero of the function with multiplicity 2. Jan 3­1:07 PM
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6­2 Day 2 Polynomials and Linear Factors 2011
January 12, 2011
For each function, find any multiple zeros and state the multiplicity.
f(x) = (x ­ 2)(x + 1)(x +1)2
y = x3 ­ 4x2 + 4x
Jan 3­1:11 PM
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6­2 Day 2 Polynomials and Linear Factors 2011
January 12, 2011
Jan 3­1:14 PM
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6­2 Day 2 Polynomials and Linear Factors 2011
January 12, 2011
HOMEWORK
p. 317 #16­20 ﴾do not graph﴿, 21­36
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