polynomials

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

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
.

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.

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

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:

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

Multiplying Polynomials
Special Products

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

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.

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

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.

polynomials

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