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
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 9x2
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.