An Algebraic expression that contains only one term is called a monomial.
Example: 2x³, 8xy, -5c, -2, etc
An Algebraic expression that contains only two terms is called a binomial.
Example: 2x-3y, l²-m², 2-3y²z, a+b, etc
An Algebraic expression that contains only three terms is called a trinomial.
Example: x+y+z, 3a²-b²-c, l²m-m²n-n, 3x³-2y²-z,etc
How do you remember the names?
Think about cycles!
An algebraic expression that contain finite number of terms with non- zero coefficients is called a polynomial. In other words it is an expression that contains finite number number of terms with combination of variables, whole number exponents of variables and constants.
Example: a+b+c+d, 7xy, 2x-3y-z, 3x⁵;+4x⁴-5x³-6x²+3x-5,etc
Degree of a Polynomial:
The monomials in the polynomials are called the terms. The highest power of the terms is the degree of the polynomial.
The coefficient of the highest power of x in a polynomial is called the Leading Coefficient of the polynomial.
Example: 2x⁵-x⁴+7x³-6x²+12x-4 is a polynomial in x.
Here we have six monomials 2x⁵, -x⁴, 7x³, -6x², 12x and -4 which are called the terms of the polynomial.
Degree of the polynomial is 5.
The Leading Coefficient of the polynomial is 2.
Like terms and Unlike terms:
Like terms contain the same variables having same powers.
Unlike terms contain different variables having different powers.
Consider the following Expression:
2x²+3x-4 All are unlike terms.
2a²-3a² These are like terms.
Look at the following expression:
3x, 5x², 2xy, -70x, -7, -3y², -3x², -20yx, 20, 4x, 3y
We Can list out the Like terms as:
- 3x, -70x and 4x
- 5x² and -3x²
- 2xy and -20yx
- -7 and 20.