Intro to polynomials.notebook
December 16, 2015
REVIEW: Please read quietly and be ready to discuss the comparison of Algebraic and Polynomial expressions! Intro to polynomials.notebook
December 16, 2015
Polynomials
3x3 + 4x2 - 5x + 6
term
How many are there??
12,
* x must be in the numerator
** variable must have a monomial* has 1 term whole # exponent 2
*** No variable exponents
4x,
6x ,
x
8
binomials have 2 terms
2
-2x + 3,
3x - 5,
3
10 - x
trinomials have 3 terms
2
x - 2x + 2,
2
-3x + 4x - 1
Intro to polynomials.notebook
December 16, 2015
What type of polynomial is each of these examples?
Intro to polynomials.notebook
December 16, 2015
There are 3 terms in this expression:
2
1
3
2x2 + 3x - 4
leading term
constant
The number in front of the variable is called the
coefficient
7x3
What is the coefficient of the following:
a) 2x
b) -5a
c) n
d) -y
Degree of Polynomials
The degree of a term is the sum of its exponents.
What is the degree of each term? NOTE: The degree of a
nonzero constant term is 0!!
a) 5x3
b) 2x2y
c) -17
d) xy5z6
The DEGREE of a polynomial is the degree of its
highest term.
What is the degree of each polynomial?
e) 4n - 5
f) 3x4 - 5x2 + 6
g) 9
h) x2y + xy - 5xy2
Intro to polynomials.notebook
December 16, 2015
Polynomials are usually written with the term with the highest degree first, the next highest second and so on. Constant terms are always LAST! This is called descending order.
Write the following in descending order:
a) 8 ­ x2 + x b) a + 2a3 ­ 7a2 ­ 6 + 10a4
Write the degree, the type (monomial, binomial, or trinomial)
and put the expression in descending order.
Expression
1) 8 - 4x + 3x
2
2) 15 + 3x
2
3) -x + 5x
4
2
5
4) 7x + 3 + x + x
4
5) 3x - 2x
3
6) 4x - 3 + x
5
Degree
Type
Descending Order