specialist maths polynomials week 1. definitions
TRANSCRIPT
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Specialist Maths
Polynomials
Week 1
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Definitions
rm.in that te variable theofpower theis terma of degree The
.polynomial in thepower highest theis polynomial theof degree The
power.highest with the variable with the term theis termleading The
valiable.a offront in constant theist coefficienA
powers. integral positive have variables thehererelation w a is polynomialA
0 where
Quartic
Cubic
:Quadratic
:Linear
:Examples
234
23
2
a
edxcxbxax
dcxbxax
cbxax
bax
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Addition and subtraction of polynomials (Ex 3A)
104
64243
32243
Example
23
223
223
xxx
xxxx
xxxx
124
3243
3243
Example
23
223
223
xxx
xxxx
xxxx
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Multiplication (Ex3A)
3243
Example223 xxxx
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Multiplication Solution
3243
Example223 xxxx
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Synthetic Multiplication (Ex 3A)
3243
Example223 xxxx
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Synthetic Multiplication Solution
3243
Example223 xxxx
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Division of Polynomials
algorithm
division thecalled is this
)()()()(
)(
)()(
)(
)(
xRxQxdxP
xd
xRxQ
xd
xP
remainder)(
quotient)(
divisor)(
polynomial)(
where
xR
xQ
xd
xP
5
46
5
46
5
34
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Example 1(Ex 3B1)
3
3323
x
xxx
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Solution 1
3
3323
x
xxx
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Example 2 (Ex 3B1)
2
12 24
x
xxx
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Solution 2
2
12 24
x
xxx
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Example 3 (Ex 3B2)
1
142
34
xx
xxx
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Solution 3
1
142
34
xx
xxx
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Synthetic Division (Ex 3B3)
2
12
Example24
x
xxx
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Synthetic Division Solution
2
12
Example24
x
xxx
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Example 4 (Ex 3B3)
3
122 34
x
xxx
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Solution 4
3
122 34
x
xxx
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Example5 (Ex 3B3)
12
532 34
x
xxx
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Solution 5
12
532 34
x
xxx
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Roots, Zeros and Factors
).( of zero a is then ,0)( If xPP
).( ofroot a is then solution, a
is If .0)( solve When we
xP
xxP
)()()(
such that )(Q polynomial a exists
e then ther),( offactor a is )( If
xQxxP
x
xPx
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Example 6 (Ex 3C)
xxx 52 of zeros theall Find 23
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Solution 6xxx 52 of zeros theall Find 23
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Example 7 (Ex 3C)
102
of factorslinear the theall Find2 xx
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Solution 7
102
of factorslinear the theall Find2 xx
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Example 8 (Ex 3C)
i23 and,3
2 rootswith
polynomial cubic real all Find
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Solution 8
i23 and,3
2 rootswith
polynomial cubic real all Find
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Example 9 (Ex 3C)
ii 2 and,21 rootswith
spolynomial quartic real all Find
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Solution 9
ii 2 and,21 rootswith
spolynomial quartic real all Find
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This Week
• Text P80 – 89
• Ex3A Q1-3;
• Ex3B1Q1-3;
• Ex3B2 Q1-3;
• Ex3B3 Q1,2;
• Ex3C Q1-6