Let us look at some key terms that pertain to Polynomials before we deep dive into the study of Polynomials.
Constant: A number having a fixed numerical value
Example: 3, \cfrac{4}{5}, 4.2, 6.\overline{3}
Variable: A number which can take various numerical values
Example: x, y, z
Algebraic Expression: A combination of constants and variables connected by arithmetic operators
Example: 2x^2 + 7, 5x^3 + 4xy + 2xy^2 + 7, etc
Terms: Several parts of an algebraic expression separated by + or - signs are called the terms of the expression.
Example: In the expression 9x + 7y + 5, 9x, 7y, and 5 are terms.
Coefficient of a Term: In the term 8x^2, 8 is the numerical coefficient of x^2 and x^2 is said to be the literal coefficient of 8.
Like Terms: Terms having the same literal coefficients are called Like Terms.
Example: 8xy, 9xy, and 10xy are Like Terms and 9x^2, -10x^2, and 5x^2 are Like Terms.
Unlike Terms: Terms having different literal coefficients are called Unlike Terms.
Example: 8xy, 9x^2, and 10xy^2 are Unlike Terms.
Polynomial: An algebraic expression in which the variables involved have only non-negative integral powers.
Example: 4x^2 + 2x + 1, 5x^3 + 16x^2 + 9
Note - The expression 3x^3 + 4x + \cfrac{5}{x} + 6x^ \frac {3}{2} is not a polynomial, since it has powers of x which are negative and fractions.
A polynomial that contains only one variable is known as a polynomial in that variable.
Degree of a Polynomial in one variable: The highest power of the variable in a polynomial of one variable is called the degree of the polynomial.
Example: (i) 2x^3 + 3x^2 + x + 8 is a polynomial of degree 3.
(ii) 8x^5 + 6x^3 + 7x is a polynomial of degree 5.
Types of Polynomials with Respect to Degree
(1) Linear polynomial: A polynomial of degree one is called a linear polynomial.
Example: 2x + 5, 6y - 9, 7z + 8, etc.
(2) Quadratic polynomial: A polynomial of degree two is called a quadratic polynomial.
Example: 6x^2 + 5x + 4, 8y + 7y^2 + 9, etc.
(3) Cubic polynomial: A polynomial of degree three is called a cubic polynomial.
Example: 7x^3 + 8x^2 + 5x + 3, 8z^3 + 9z + 3, etc.
Types of Polynomials with Respect to Number of Terms
(1) Monomial: An expression containing only one term.
Example: 6x, 5x^3, 7xyz^3, etc.
(2) Binomial: An expression containing two terms.
Example: 6x^2 + 5y, 2xy + 5, etc.
(3) Trinomial: An expression containing three terms.
Example: 7x + 2y - 4z , 4z^3 + 5xy + 9, etc.
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