Unit 7 Day1: Introduction to
Polynomials
Essential Questions: What are polynomials? How do we
classify them? How can we evaluate them?
Vocabulary
A polynomial is an expression with many terms. A polynomial
written in standard form means the terms are written in
descending order according to the exponents. The following is
an example of a polynomial
written
in
standard
form:
2x3 + 5x2 – 4x +
7
Degree: highest exponent (3)
Leading Coefficient: number in front of the variable with the
highest degree (2)
Constant: number not connected to a variable; stays “constant”
(7)
Degree
2x3 + 5x2 – 4x + 7
Leading
coefficient
Constant
Writing Polynomials in
Standard Form
2
2x
5 - 2x
-2x + 5
x + 5x2 - 7 - 4x3
3
2
-4x + 5x + x 7
-4 +
2
2x - 4
3
x
+
2
5x
- 7 - 4x +
4
6x
4
3
2
6x + x + 5x - 4x 7
Classifying Polynomials
The degree of a polynomial tells us what type of polynomial it is.
x0
constant
x1
linear
x2
quadratic x3
cubic
x4
quartic
x5 or higher
polynomial
The number of terms of a polynomial tells us what type of
polynomial it is.
1 term
monomial
2 terms
binomial
3 terms
trinomial
4 or more terms
polynomial
Classifying Polynomials
x+1
2
2x
+ 3x - 5
leading coefficient: 1
leading coefficient: 2
constant: 1
degree: 1
two terms
linear binomial
2
6x
constant: -5
degree: 2
three terms
quadratic trinomial
3
2x -
2
3x
+ 4x - 5
leading coefficient: 6
leading coefficient: 2
constant: 0
degree: 2
one term
constant: -5
degree: 3
four terms
cubic polynomial
quadratic monomial
Classifying Polynomials
2
x
+5
3
2x
+
2
3x
-5
leading coefficient: 1
leading coefficient: 2
constant: 5
degree: 2
two terms
constant: -5
degree: 3
quadratic binomial
5
cubic trinomial
4
3
2x - 3x + 2x - 6
leading coefficient: 5
leading coefficient: 2
constant: 5
degree: 0
one term
constant: -6
degree: 4
four terms
constant monomial
quartic polynomial
three terms
Evaluating Polynomials
3
2x
2
3x
+
- 5; x = 2
3
2
2(2) + 3(2) - 5
2(8) + 3(4) - 5
16 + 12 - 5
28 - 5
23
2x4 - 3x3 + 2x - 6; x = -1
4
2(-1)
3
3(-1) +
2(-1) - 6
2(1) - 3(-1) - 2 - 6
2+3-2-6
5-2-6
3-6
-3
Summary
In the “summary” portion of your notes,
please respond to the essential questions.