Transcript 5.1 Introduction to Polynomials

4.3 Polynomials
• Monomial: 1 term (axn with n is a nonnegative integers)
Ex: 3x, -3, or 4y2
• Binomial: 2 terms
Ex: 3x - 5, or 4y2 + 3y
• Trinomial: 3 terms
Ex: 4x2 + 2x - 3
• Polynomial: is a monomial or sum of
monomials
Ex: 4x3 + 4x2 - 2x - 3 or 5x + 2
Identify monomial, binomial, trinomial, or
none
x4
-2x + 4
3x2
-2x2 - 2x +1
4x3 + 4x2 - 2x - 3
4 + (1/2)x
monomial
binomial
monomial
trinomial
None (polynomial)
binomial
•
•
•
•
•
•
Term: each monomial of the polynomial
Degree: exponents
Degree of polynomial: highest exponent
Coefficient: number in front of variables
Constant term: the term without variable
Missing term: the term that has 0 as its
coefficient 0
• Ex:
Term:
-3x4 – 4x2 + x – 1
-3x4 , – 4x2 , x, – 1
Degree
4
2
1
0
Coefficient
-3
-4
1
Degree of this polynomial
is 4
Constant term:
is -1
Missing term (s):
is x3
-1
• Descending order: exponents decrease
from left to right
• Ascending order: exponents increase
from left to right
• When working with polynomials, we often
use Descending order
•
Arrange in descending order using power
of x
1) -6x2 – 8x6 + x8 + 3x - 4
= x8– 8x6 - 6x2 + 3x - 4
Missing terms are: x7, x5, x4, x3
2) 5y2 + 4y + 2y4 + 9
= 2y4 + 5y2 + 4y + 9
Missing terms are: y3
Collecting Like Terms
• Like terms:
4x and 3x
5xy and -6xy
2x2 and x2
When add or subtract like-term, add or subtract only
the coefficients of the terms, keep the same
variables
1) -6x4 – 8x3 + 3x - 4 + 5x4 + x3 + 2x2 -7x
= -6x4 + 5x4 – 8x3 + x3 + 2x2 + 3x -7x -4
=
-x4
- 7x3 + 2x2
- 4x
-4
2) -6x4 – 8x3 + 3x - 4 - 5x4 - x3 - 2x2 +7x
= -6x4 - 5x4 – 8x3 - x3 - 2x2 + 3x +7x - 4
= -11x4 - 9x3 - 2x2 +10x -4