Download In this unit we will study algebraic expressions called

Mathematics 10
Kim
CH5: Polynomials
In this unit we will study algebraic expressions called polynomials.
In algebra, a letter that represents one or more numbers is called a variable.
5
Expressions like 2a-b + 4 or 𝑥 is called an algebraic expressions. Certain algebraic expressions are called polynomials as
explained below.
5.0 Review of Classification, Terms, and Addition and Subtraction involving Polynomials
Polynomial: One term or the sum of terms whose variables have whole-number exponents
- A polynomial consists of one or more TERMS (which are separated by + or – signs).
- The number that multiplies the variable is called the coefficient.
Eg.
2 4
𝑥
5
+ 𝑥3 + 𝑥 − 6
1. Identify whether each expression is a polynomial.
3𝑥 2 + 𝑥 + 5
1
𝑥
√𝑥 + 3
𝑥 4 + 𝑥𝑦 + 𝑦 2
Like Terms: terms that have the same variable raised to the same exponent
Eg. 3a, 7a and a are like terms.
-
Unlike terms have different variables or the same variable raised to different exponents.
1
Eg. 2𝑥 3 , 5 𝑥 2 , and −4𝑥 are unlike terms.
-
1
2x3, 5 𝑥 3 and − 4𝑥 3
4x and 4y are unlike terms.
Like terms can be added or subtracted to produce a single term.
2. Simplify.
a) 𝑛3 + 4𝑛2 − 2 − 𝑛2 − 3𝑛3
=-4n3+3n2-2
b) 2𝑥 4 + 5𝑦 4 + 𝑥 2 𝑦 + 𝑥𝑦 2 − 2𝑥 2 − 2𝑦 2
no like terms, can’t simplify further
Mathematics 10
Kim
Classification of Polynomials:


by the number of terms:
-
monomial: A polynomial with 1 term
eg. x, ab,
-
binomial: A polynomial with 2 terms
eg. 5+j, 3x+3
-
trinomial: A polynomial with 3 terms
eg. 7m2 +2m +1
by degree:
- The degree of a term is the sum of the exponents of its variable(s).
Eg.
Ex. 1
2x5
3xy4
-
The degree of a polynomial is the degree of the term with highest degree.
-
A constant term (a number) has a degree zero.
-
The coefficient of the term with highest degree is called the leading coefficient.
Complete the following table.
Polynomial Expression
4𝑥 + 3𝑥𝑦
2𝑎 − 4𝑏 + 7𝑐
𝑥 2 + 3𝑥 + 4
√2𝑥
2𝑥 3 + 3𝑥 2 𝑦 + 3𝑦 2 − 8
#of Variables
# of Terms
2
3
1
1
2
2
3
3
1
4
Name of Polynomial
By # of Terms
monomial
trinomial
Trinomial
monomial
Polynomial
Degree
2
1
2
1
3
Mathematics 10
Kim
MA10 Ch5
WS 5.0 Review
Name:
1. Identify as a monomial, a binomial, or a trinomial.
a) 𝑥 + 1
b) 3
c) 2𝑥 2 + 2𝑥 + 2
b) 2ab
c) 7a2bc2
b) 8𝑚−2
c) √2
2. State the degree of each monomial.
a) 5a
3. Circle all polynomial expressions.
1
a) 2 𝑥 + 1
7
d) 𝑥 3
e)
𝑥2
f) 𝑥 4 + 𝑦 3 + 1.5
5
4. Complete the following table.
Polynomial
Expression
2𝑦 3 + 𝑦 4 + 11
9𝑎𝑏 + 4𝑐 + 5𝑥
10
2 3 3
𝑥 𝑦𝑧 + 𝑥 2 𝑦 2
5
# Variables
Name of
Polynomial
Degree
Leading
Coefficient
Mathematics 10
Kim
5. Simplify.