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62 Day 2 Polynomials and Linear Factors 2011
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January 12, 2011
Jan 312:26 PM
62 Day 2 Polynomials and Linear Factors
ObjectiveWrite a polynomial function from its zeros.
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Review:
1. Write this polynomial in standard form: ﴾x + 1﴿﴾x 2﴿﴾x+3﴿
2. Write this polynomial in factored form: x3 x2 12x
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What are ZEROS of a graph?
ZEROS are:xintercepts ﴾where the graph crosses the xaxis﴿rootssolutions
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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 or x + 1 = 0 or x + 3 = 0
x = x = x =
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Find the zeros of y = ﴾x 7﴿﴾x 5﴿﴾x 3﴿
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You can reverse this process and write linear factors when you
know the zeros!
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Write a polynomial function in standard form with zeros at 2, 3, and 3.
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Write a polynomial function in standard form with zeros at 4, 2, and 0.
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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.
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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.
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For each function, find any multiple zeros and state the multiplicity.
f(x) = (x 2)(x + 1)(x +1)2 y = x3 4x2 + 4x
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HOMEWORK
p. 317 #1620 ﴾do not graph﴿, 2136
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