Algebraic Expression | Basic | Algebraic Expression
A mathematical expression that exists in the form of variables and constants along with mathematical operations viz., addition, operation, multiplication and division is called algebraic expression. For example
2x7 – 5xy + 3y + 12 (x, y are variables and 2, 5, 3 & 12 are constants)
xy3z + 37x – 100 (x, y, z are variables and , 37 & – 100 are constants]
Polynomials
An algebraic expression is said to be polynomial if and only
- Coefficients are real numbers (Natural Number, Whole Number, Integers & Rational Numbers)
- Exponents in each terms of the variable are non-negative integers.
For example – 2x7 – 5xy + 3y + 12
Here the coefficients are 2, –5, 3 and 12 are real numbers
& exponents are 7, 1 and 0 are non- negative integers
(Exponents of the variable x are 7, 1 & 0 and exponent of y is 1. All these are non-negative integers)
Hence, 2x7 – 5xy + 3y + 12 is a polynomial
[Note: Fourth term of the polynomial is 12 which can be written as 12 = 12 × 1 = 12x0
{x0 = 1} and so exponent of x is 0]
Let us take another example which seems to be polynomial but it is actually not a polynomial.
∛x + 5y + 10 is not a polynomial because exponent of x is and it is not an Integer.
Various forms of Polynomials
Monomial: The word MONO Means 1(One). So, any polynomial having only 1(One) Term is refer to as Monomial. For example: –3x4, 28p2q and –100, etc are Monomials.
Binomial: The word Bi means 2(Two). So, any polynomial having only 2(Two) Terms is refer to as Binomial. For example: 3x4 + 3 and 28p2q –100, etc are Binomials.
Trinomial: The word Tri means 3(Three). So, any polynomial having only 3(Two) Terms is refer to as Trinomial. For example: 3x4 + 3 + 28p2q is a Trinomial.
Quadrinomial: The word Quadri means 4(Four). So, any polynomial having only 4(Four) Terms is refer to as Quadrinomial. For example: 3x4 + 3 – 28p2q –100y, etc is a Quadrinomial.
[Note: The word Poly means many]
How to express Decimal Number as Rational Number?
