# Introduction to polynomial class 10th #

Introduction to Polynomials
5.2
1. Identify monomials.
2. Identify the coefficient and degree of a monomial.
3. Classify polynomials.
4. Identify the degree of a polynomial.
5. Evaluate polynomials.
6. Write polynomials in descending order of degree.
7. Combine like terms.

Objective 1
Identify monomials.

Monomial: An expression that is a constant, a
variable, or a product of a constant and
variable(s) that are raised to whole number
powers.
Exponent can’t be negative!
Exponent can’t have fractions!
a number
x, y
Multiply a
number and a
variable

When an equation in one variable is solved the answer is a point on a line.
Is the given expression a monomial?
18
3
4 
 x
b
0.4a
– 2
x
3
Yes
Yes
No No

Objective 2
Identify the coefficient and degree of
a monomial.

Coefficient of a monomial: The numerical
factor in a monomial.
Degree of a monomial: The sum of the
exponents of all variables in a monomial.

Identify the coefficient and degree of each monomial:
2
8p
18
m
-
2
7
6 uv
.

5
3
2 a 2
4
C: -1
D: 1
C: 8
D: 2
C: 18
D: 0
C: -6.7
D: 3
C: 23 = 8
D: 5
C: 16
D: 0
x0

Objective 3
Classify polynomials.
Objective 4
Identify the degree of a polynomial.

Polynomial: A monomial or an expression that
can be written as a sum of monomials.
Examples: 4x, 4x + 8, 2x2 - 5xy + 8y
Polynomial in one variable: A polynomial in
which every variable term has the same
variable.
Example: x2 – 5x + 2

Binomial: A polynomial containing two terms.
Trinomial: A polynomial containing three terms.
Degree of a polynomial: The greatest degree of
any of the terms in the polynomial.

Identify the type of polynomial and the degree:
2
4ab
1
3
4 3

 n
n
z
9x
- 2

4
9 2
3


 x
x
x
x
y
6
8  j
j
j
j 14
21
16
5
22 4
2
3




Monomial
D: 3
Binomial
D: 2
Trinomial
D: 3
Polynomial
D: 3
Not a polynomial Polynomial
D: 4

Objective 5
Evaluate polynomials.

Evaluate each of the following:
y
,
x
for
y
x 4
1
2 2




2
1
2



 b
,
a
for
b
a
4
3 


 n
for
n
n2
-2(-1)2(4) = -8
(-4)2 – (-4) – 3 = 16 + 4 – 3 = 17
- (-1)2 (2) = - (1)(2) = -2

Objective 6
Write polynomials in descending
order of degree.
Combine like terms.
Objective 7

Writing a Polynomial in Descending Order of Degree
Place the highest degree term first, then the next
highest degree, and so on.

Write the polynomial in descending order.
2 3 4
2 5 7 4
    
x x x x
4
4x 3
x
 2
7x
 x
2
 5


Combine like terms and write the resulting polynomial
in descending order of degree.
3 2 3 3
4 6 3 7 4 3 6
x x x x x x
      
5 2 5 2
6 2 3 1 3 3
      
a a b b a b a b
3
8x
5
3
2 2
5

 b
a
a
2
6x
 x
2
 4


19
Classify the expression
a) Monomial
b) Binomial
c) Trinomial
d) None of these
2 3
3 5.

x y
5.2

20
Evaluate when x = –3.
a) –118
b) –10
c) 10
d) 134
3 2
3 5 8
 
x x
5.2

21
Evaluate when x = –3.
a) –118
b) –10
c) 10
d) 134
3 2
3 5 8
 
x x
5.2

22
Identify the degree of the polynomial.
a) 3
b) 5
c) 6
d) 7
3 2 4 6 5
6 5 8 4
  
x x y x y y
5.2

23
Identify the degree of the polynomial.
a) 3
b) 5
c) 6
d) 7
3 2 4 6 5
6 5 8 4
  
x x y x y y
5.2

# Introduction to polynomial class 10th #

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