1. Fundamental Concepts of Algebra2
GEETHA VENKATARAMAN

3. Algebraic expressions are composed of variables and constants
Variables: The letters used in algebra are called variables or literal numbers or simply literals. They do not have a fixed value.
Constant: A symbol with a fixed numerical value in all situations is called a constant. x

4. Verbal phrases can be expressed in the form of algebraic expressions
The sum of six and a number
6 + x
Eight more than a number
y + 8
A number plus six
n + 6
A number increased by seven
x + 7
A number decreased by five
n – 5
Ten times a number
10.n or (10n)

5. Products are the results of multiplication of constants, variables or both
8𝑥𝑦, 3x, 5y
Factor: Each constant and each variable multiplied together to form a product is called a factor of that product.
Product
Factor
8xy
8, x, y 3x
3, x 5y
5, Y
Coefficient: Any factor or group of factors of a product is known as the coefficient of the remaining factors.
𝐼𝑛 𝑡ℎ𝑒 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 8𝑥𝑦
Factor
Coefficient of 8 xy 8𝑥 y 8x
Numerical Coefficient:
If factor is a numerical quantity

6. A term is a constant or a variable or a product or a quotient of constants and variables.
5+𝑧+ 3𝑥+ 3 𝑦
Term
Type of term 5
a constant. z
a variable 3x
the product of a constant and a variable
3 y
the quotient of a constant and a variable

7. Terms in an algebraic expression can be like or unlike
Unlike Terms: The terms that do not have the same literal coefficients are called unlike terms.
Like Terms: The terms having the same literal coefficients are called like terms
3𝑥 𝑎𝑛𝑑 7𝑥
Like
6𝑤 𝑎𝑛𝑑 8𝑦
Unlike
5, 89, 𝑎𝑛𝑑 100
Like
5 𝑎𝑛𝑑 8𝑥
Unlike

8. A polynomial is an algebraic expression with one or more terms
Types of Polynomials
Monomial: An algebraic expression containing only one term
Example : 3x, 4z, 2y, 5t
Multinomial: An algebraic expression containing more than one term
Binomial: An algebraic expression containing two terms
Example: 3y + 5x, 4z – 6y, 2x + 6x
Trinomial: An algebraic expression containing three terms
Example: 3x + 4z – 3n

9. Degree of a polynomial
Power or Exponent of a quantity: When a quantity is multiplied by itself a number of times, the product is called a power of that quantity
8× 𝑥 ×𝑥 =8 𝑥 2
In a polynomial of one variable, degree is the greatest of the exponents ( powers) of its various terms
For the polynomial 𝟓 + 𝒙 𝟐 +𝟑 𝒙 𝟓
Exponent of the term 𝑥 2 =2
Exponent of the term 3 𝑥 5 =5
The degree of the given polynomial is 5
In a polynomial of two or more variables, degree is the greatest of the sum of the powers of all variables used in each term
For the polynomial 𝟑𝒙 + 𝒙 𝒚 𝟐 − 𝟕𝒚𝒛
Sum of the powers of the variables in 𝑥 = 1
Sum of the powers of the variables in 𝑥 𝑦 2 = 1+2 = 3
Sum of the powers of the variables in 𝑦𝑧 = 1+1 = 2
The degree of the given polynomial is 3