This document defines key terms related to polynomials including monomial, binomial, trinomial, constant, coefficient, and degree. It also describes methods for multiplying polynomials including multiplying monomials, multiplying polynomials using FOIL, squaring binomials, and multiplying the sum and difference of binomials. Finally, it provides examples of dividing monomials.

1. Submitted by:
Litty Cherian
class:1BEd
Option: Mathematics
Roll No:22
Mangalam College of Education
Submitted to:
Mrs.Sijji Jose
Dept. Educational technology

2. DEFINITIONS
Term
A number or a product of a number and variables raised to a power.
eg : 3, 5𝑥2, -2𝑥, 9𝑥2y.
Coefficient
The numerical factor of each term.
eg :5𝑥2
, -2𝑥 ,9𝑥2
𝑦.
Constant
The term without a variable.
eg : 3, -6, 5, 32.
Polynomial
A finite sum of terms of the form axn
, where a is a real number and n is a whole number.
eg : -15x2
+ 2x2
.

3. Monomial
A polynomial with exactly one term.
eg: 𝑎𝑥2
, 2𝑥4
, -9m, 9𝑥2
y.
Binomial
A polynomial with exactly two term.
eg: 𝑥-8, -2𝑥 + 9𝑥2
y.
Trinomial
A polynomial with exactly three term.
eg: 𝑥2 + 𝑥 − 8, 5𝑥2 + 2𝑥 − 7.

4. The Degree of a Term with one variable is the exponent on the variable.
The Degree of a Term with more than one variable is the sum of the exponents
on the variables.
The Degree of a Polynomial is the greatest degree of the terms of the polynomial
variables.
2
5x  2,
9m  1
2
7x y  3,
5 4
9mn z 10
3
2 3 7x x  3,
4 2 2 3
2 5 6x y x y x   6

5. Multiplication

6. Multiplying Monomials by Monomials
Examples:
10 9x x  2
90x
 3 7
8 11x x  10
88x
Multiplying Monomials by Polynomials
 2
4 4 3x x x   3
4x 2
16x 12x
  3 2
5 3 2x x x   
5
15x 4
5x 3
10x
Examples:

7. Multiplying Two Polynomials
Examples:
1.
2.
  2
5 10 3x x x    3
x 2
10x 3x 2
5x 50x 15
3
x=
2
15x 47x
  2
4 5 3 4x x x    3
12x 2
16x 2
3x 4x 15x 20
= 3
12x 2
13x 11x 20

8. Multiplying Polynomials
Special Products

9. Multiplying Two Binomials using FOIL
First terms Outer terms Inner terms Last terms
  3 4x x   2
x 4x 3x 12
2
x 7x 12
  7 4x x   4x 28
3x
=
2
x 7x
=
2
x 28

10. Squaring Binomials
 
 
2 2 2
2 2 2
2
2
a b a ab b
a b a ab b
   
   
 
2
4 5x   2
16x  2 20x  25  2
16 40 25x x 
Example
1.

11. Multiplying the Sum and Difference of Two Binomials
   2 2
a b a b a b   
Examples
1.
2.
  9 9x x   9x2
x 9x 81  2
81x 
   88 xx 642
x

12. Dividing by a Monomial
where 0
a b a b
c
c c c

  
8 6 4
3
21 9 12
3
x x x
x
 

8
3
21
3
x
x
6
3
9
3
x
x

4
3
12
3
x
x
 
5
7x 3
3x 4x
Examples:
1.