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7/27/2019 Chapter 3 Polynomials S
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6.1 POLYNOMIALS 6.2 REMAINDER THEOREM,
FACTOR THEOREM AND ZEROS
OF POLYNOMIAL
6.3 PARTIAL FRACTIONS
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LEARNING OUTCOMES
Determine the degrees and coefficients of
polynomials.
Carry out elementary operations on polynomials.
Use the remainder and factor theorems.
Find the roots and zeros of a polynomial.
Express rational functions in partial fractions.
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3.1 POLYNOMIALS
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Polynomial Specialname Degree Leadingcoefficient(a)
(b)
(c)4
(d)
(e)
91242
xx
1053x
xx 924
79 x
Quadratic
Cubic
4
Constant
5
-2
9
4
2
4
1
Quartic
Linear
3
0
Ex. 3.1:
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Equality of Two Polynomials and Operations on
Polynomial
Two polynomial are equal if coefficients of similar
terms are the same.
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Two polynomials can be added, subtracted and
multiplied.
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The quotient of polynomials will also be consideredwhere the process of division of polynomials by long
division will be discussed.
where the degree ofR(x) is less than the degree ofD(x).
The polynomial Q(x) is called the quotient and R(x) the remainder.11
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35841223
xxxx
22x
2324 xx
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35841223
xxxx
2324 xx
xx 362
xx 56 2
xx 322
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35841223
xxxx
23 24 xx
xx 362
xx 562
32 x
12 x
2
1322
xx
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REMAINDER THEOREM
The remainder theorem offers a method of finding
the remainder without going through the process of
division.
TheoremTHE REMAINDER THEOREM
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TheoremTHE FACTOR THEOREM
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DefinitionZEROS OF POLYNOMIAL
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Solution
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3.3 PARTIAL
FRACTIONS
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PROPER FRACTION
Ratio of two polynomials when the degree of the
numerator is less than the degree of the denominator.
IMPROPER FRACTION
Ratio of two polynomials when the degree of the
numerator is greaterthan the degree of the
denominator.
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Two simple algebraic fractions can be combined to
become a single compound fraction:
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There are some rules to express fractional polynomial
functions as a sum of partial fractions:
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e) Degree of the numerator is the same or higher
than the denominator
Long division is carried out so that the degree of
the numerator becomes less than thedenominator.
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