Transcript 7.1: Polynomial Degree and Finite Differences

7.1: Polynomial Degree and
Finite Differences
Day One
Polynomials
A ______________is
polynomial a sum of terms containing
the same variable raised to different powers.
Each term is a product of numbers and
____________.
variables
The exponents are nonnegative integers and the
coefficients are ______ numbers.
real
Examples of Real Numbers:
2
3
10
2

Polynomials Continued
function is a polynomial set
A polynomial ___________
equal to a second variable. Example: y=2x+7
Examples
Can the following be terms of a polynomial?
a)
b)
c)
d)
3x
3
3x
g)
3
x
4
e)
4x
2
3x
h)
4x
5x
f)
32
6
2
x
4
Types of Polynomials
one terms.
Monomial: A polynomial with ______
Binomial: A _______________
polynomial with two terms.
_______________:
Polynomial A polynomial with three or more
terms.
Polynomials Continued
The ___________
degree of a polynomial is the power of
the term that has the greatest exponent.
Examples:
1) 2x7+3x3-5+2x
2) 5x+7x2+12-2x3
3) 5x-7
4) 11x5+20x3-4x6
General Form
General From is when the polynomials are
in ________________
decreasing order from left to right.
Examples: Which of the following are in
general form?
1. x2 + 4x - 5
2. -5x +4 - 2x3
3. X4 - 4
4. 8x2 - 4x + x3 - 6x4 + 7
Finite Differences
A method of determining the __________
degree
of a polynomial.
Example: 4x-1
X
0
1
Y
-1
3
2
7
3
11
4
4
4
Example: 3X2+2X+4
X
Y
0
4
1
9
2
20
3
37
4
60
5
89
5
11
17
23
29
6
6
6
6
Finite Differences Continued
Example: y = -2x3 + 3x2 + 4x - 5
x
y
0
-5
1
0
2
-1
3
-20
4
5
-69
-160
5
-1
-19
-49
-91
-6
-18
-30
-42
-12
-12
-12
Finite Differences Continued
Example: What is the degree of the polynomial
represented by the following data?
x
y
0
11
1
8
2
9
3
14
4
23
-3
1
5
9
4
4
4
Second Degree Polynomial