specialist maths polynomials week 1. definitions
TRANSCRIPT
Specialist Maths
Polynomials
Week 1
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
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
Multiplication (Ex3A)
3243
Example223 xxxx
Multiplication Solution
3243
Example223 xxxx
Synthetic Multiplication (Ex 3A)
3243
Example223 xxxx
Synthetic Multiplication Solution
3243
Example223 xxxx
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
Example 1(Ex 3B1)
3
3323
x
xxx
Solution 1
3
3323
x
xxx
Example 2 (Ex 3B1)
2
12 24
x
xxx
Solution 2
2
12 24
x
xxx
Example 3 (Ex 3B2)
1
142
34
xx
xxx
Solution 3
1
142
34
xx
xxx
Synthetic Division (Ex 3B3)
2
12
Example24
x
xxx
Synthetic Division Solution
2
12
Example24
x
xxx
Example 4 (Ex 3B3)
3
122 34
x
xxx
Solution 4
3
122 34
x
xxx
Example5 (Ex 3B3)
12
532 34
x
xxx
Solution 5
12
532 34
x
xxx
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
Example 6 (Ex 3C)
xxx 52 of zeros theall Find 23
Solution 6xxx 52 of zeros theall Find 23
Example 7 (Ex 3C)
102
of factorslinear the theall Find2 xx
Solution 7
102
of factorslinear the theall Find2 xx
Example 8 (Ex 3C)
i23 and,3
2 rootswith
polynomial cubic real all Find
Solution 8
i23 and,3
2 rootswith
polynomial cubic real all Find
Example 9 (Ex 3C)
ii 2 and,21 rootswith
spolynomial quartic real all Find
Solution 9
ii 2 and,21 rootswith
spolynomial quartic real all Find
This Week
• Text P80 – 89
• Ex3A Q1-3;
• Ex3B1Q1-3;
• Ex3B2 Q1-3;
• Ex3B3 Q1,2;
• Ex3C Q1-6