Polynomials Intro

1. Block 2
Polynomials Introduction

2. What is to be learned?
• What a poLynomial is
• How you know what degree a poLynomial
is
• What the big L is, and how it works

3. Spot The PoLynomial
x2
+ 4x – 2
7x + 2
sinx
5x2
-6x7
8x





degree 2
degree 7
degree 1

4. A Calculation
f(x) = 3x4
– 2x3
+ x2
– 4x + 7
f(2)?
= 3(2)4
– 2(2)3
+ 22
– 4(2) + 7
= 35
Causes a lot of tension

5. Introducing the Big L
f(x) = 3x4
– 2x3
+ x2
– 4x + 7 f(2)?
3 -2 1 -4 7

6. Introducing the Big L
f(x) = 3x4
– 2x3
+ x2
– 4x + 7 f(2)?
3 -2 1 -4 72 3
X
2
6
+
4
X
2
8
+
9
X
2
18
+
14
X
2
28
+
35

7. Introducing the Big L
f(x) = 3x4
– 2x3
+ x2
– 4x + 7 f(2)?
3 -2 1 -4 72 3
X
2
6
+
X
2
8
+
X
2
18
+
X
2
28
+
353
f(2) = 35
4 9 14

8. Introducing the Big L
f(x) = 4x4
– 5x3
+ 2x2
– 3x + 11 f(3)?
-5 2 -3 113 4
12
7
21
23
69
66
198
2094
f(3) = 209

9. PoLynomials
• Expressions with (non negative) powers of x
• Highest power gives the
• PoLynomial calculations invariably involve
The Big L
(also known as nested calculation scheme)
(by those with a sad lack of imagination)
degree

10. Calculating Function Values
With The Big L
f(2)? f(x) = 3x4
– 4x3
+ x2
– 2x + 9
3 -4 1 -2 92
X
2
6
+
2
X
2
4
+
5
X
2
10
+
8
X
2
16
+
253
f(2) = 25

11. Key Question
f(x) = 2x4
– 6x3
+ 5x2
– 4x + 16 f(3)?
-6 5 -4 163 2
6
0
0
5
15
11
33
492
f(3) = 49

12. Beware
3x4
+ 2x2
– 7x + 9
3 2 -7 9
no x3
term
0