Polynomials

posted on: 06 Mar, 2012 | updated on: 21 Sep, 2012

If the exponent of a variable in an algebraic expression is a Whole Number then it is called a polynomial. A function p(x) of the form: p(x) = an x₀ + a₁ x + a₂ x₂+ …. + a_n, where all a₀ , a₁, a₂ , an are real Numbers and n is non zero negative number (i.e. a whole number) is called a polynomial. For example : x + a, x² – a² + bx + c, x³ + 3x³ + 3x +1, z³ – 7y - 6 etc. are polynomials. If the powers of variable x are either in increasing or decreasing order, the polynomial in x is said to be in standard form.

The degree of a polynomial is the greatest exponent of that variable.

The degree of 2x + 5 is 1,

The degree of 3x² + 7x - 6 is 2 and

The degree of 6x⁵ – 3x² y³ + 7xy² is 5.

Polynomials of various degrees are:-

1. Linear polynomial: - have only one degree such as: - 3x + 5

2. Quadratic polynomial: - have at least two degree such as: - 3y² – 7y + 6

3. Cubic polynomial: - have at least three degree such as: - 3x³ – 2x² + 6x + 1

4. Bi quadratic polynomial: - have at least 4 degree such as: - x⁴ – 3x³ + 2x + 5x - 3

Number of terms in a polynomial:-

Monomial: - A polynomial containing one nonzero term. For example: - 5, 3x

Binomial: - A polynomial containing two nonzero terms. For example: - (3 + 6x), (x - 5y)

Trinomial: - A polynomial containing three nonzero terms. For example: - (8 + 3x + x ²), ( 3y – 5xy + 7xy² )

Topics Covered in Polynomials

Factoring Polynomials

posted on: 16 Jul, 2012 | updated on: 15 Sep, 2012

In mathematics, any expressions which consist of constants, variables and exponent values that are joined together by mathematical operators like addition, subtraction, multiplication, are said to be Polynomials. Exponent’s values can be 0, 1, 2, 3 and 4 ….etc. Infinite values are not possible in case of polynomials expression. For example: 7xy² – 5x + 5y³ – 15, th...Read More

Polynomial Inequalities

posted on: 18 Jul, 2012 | updated on: 16 Aug, 2012

Polynomial expression can be defined as an expression which contains number of terms and they are joined together by operators. Here we will discuss a Polynomial Inequalities. An expression that consists of constants, variables and exponent values joined together by mathematical operators like addition, subtraction, multiplication, are known as Polynomials. Infin...Read More

Graphing Polynomials

posted on: 16 Jul, 2012 | updated on: 17 Jul, 2012

Graphing is a better way to understand mathematical expressions, functions, relations etc as they are pictorial representation of any quantity. However, it is possible to graph Polynomials with one or multi variables b...Read More

Multiplying Monomials

posted on: 21 Mar, 2012 | updated on: 27 Aug, 2012

Before we study about multiplying monomials, let us first learn what monomials are. Monomials are the algebraic expressions with only one term. Examples of the monomials are 2x, 4y, xy, 4ab etc.
Now in this unit we will learn about how to multiply monomials. If we have any two monomials, we need to first bring together the constant values of both the monomials and...Read More

Dividing Monomials

posted on: 21 Mar, 2012 | updated on: 27 Aug, 2012

Before we study about dividing monomials, let us first learn that what are monomials? Monomials are the algebraic expressions with only one term. Examples of the monomials are 2x, 4y, xy, 4ab etc.
Now in this unit we will learn about how to divide monomials.
The rules of dividing the monomials are just opposite from the rules of multiplication. Thus before we procee...Read More

Adding and Subtracting Polynomials

posted on: 26 Mar, 2012 | updated on: 27 Aug, 2012

In order to Add and Subtract Polynomials, we must remember that the numerical values of the like terms are added or subtracted. In order to learn Adding Subtracting Polynomials, we must first know about like and unlike terms. The terms with the same factors of the variables, may be that they have different co-efficient are ...Read More

Special Products

posted on: 27 Mar, 2012 | updated on: 23 Jul, 2012

Special products are the identities which are expressed in form of special product. If we need to solve certain expressions by Factorization, standard identities for finding the products of the terms has been deduced in order to get the resultant products, which make the method of finding the product easy. Let us take the expression say (x + y) * (x + y). Now the above ...Read More

Multiplying a Monomial and a Polynomial

posted on: 27 Mar, 2012 | updated on: 05 May, 2012

We can multiply a polynomial with a monomial by following the rules given below,
· As we know that Monomial is basically a mixture of a constant and a variable, which contains only one term and If we talk about polynomial ,then it is an algebraic expression in which the variable involved have only non-negative integral powers is called ...Read More

Scientific Notations

posted on: 28 Mar, 2012 | updated on: 21 Sep, 2012

Scientific notation is a method of representing numbers in standard decimal form. It is a most common property used in calculators by engineers and mathematicians. Normalized scientific form represents large Numbers for many fields. It does not include calculations in un-normalized form. It is also known as exponential notation. In exponential notation ‘a’ is no...Read More

Degree, Ascending and Descending Order

posted on: 28 Mar, 2012 | updated on: 21 Sep, 2012

We find that the numbers and the literals can be arranged in ascending and descending order of the degree of the Polynomials. First we will learn about the degree of the polynomials, we say that the degree of the polynomials is the sum of the exponents of the variables.
If we have the exponents 4x² + 5x + 3, here we observe that the term of the lar...Read More

Multiplying Polynomials

posted on: 16 Apr, 2012 | updated on: 08 Jun, 2012

An expression in which variables, constants and exponent are present is known as polynomial expression. A polynomial expression contains addition, subtraction, and multiplication symbol.
For example: 3p² + 8p³ – 4p - 2 = 0, we can easily say that the given equation is a polynomial expression because the expression follows the definition of polynomial.
Before un...Read More

Finding Zeroes of Polynomials

posted on: 16 Jul, 2012 | updated on: 17 Jul, 2012

Any algebraic expression which includes variable which have only positive powers are called Polynomials. We must remember that algebraic expression is always separated by the '+' or '–' operators, which we call terms of expression.
There exist a difference between zero polynomial and the zero of the polynomial. By zero polynomial we Mean that polynomial ha...Read More