BASIC CONCEPT OF POLYNOMIAL

About "Basic concept of polynomial"

Basic concept of polynomial :

Here we are going to see some basic concepts of polynomial.

Monomial :

An Algebraic expression that contains only one term is called a monomial.

Examples :

3a, -2x2, 5xy

Binomial :

An Algebraic expression that contains only two terms is called a binomial.

Example :

x + y, 4a + 3b, 3x2 - 5xy

Trinomial :

An Algebraic expression that contains only three terms is called a trinomial.

Example :

x + y + z, 2a + 3b - 4, 2a + 3c - 5

Polynomial :

An expression containing a finite number of terms with non-zero coefficient is called a polynomial. In other words, it is an expression containing a finite number of terms with the combination of variables, whole number exponents of variables and constants.

Example :

a + b + c + d

7xy, 3abc - 10

2x + 3y + 5z

3x5 + 4x4 - 3x3 7x2 - 5 x + 4

Degree of the Polynomial :

The monomials in the polynomial 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.

2x5 - x4 + 7x3 - 6x2 + 12x - 4 is a polynomial in x. Here we have six monomials. 

Degree of the polynomial is 5.

The leading coefficient of the polynomial is 2.

In an algebraic expression, we may find the following three parts.

(i)  Terms

(ii)  Factors

(iii)  Coefficients

What is term ?

A single variable or a constant or a combination of these as a product or quotient forms a term.

Examples of terms :

5, -a, 3ab, 21/7, ........... etc

Terms can be added or subtracted to form an expression.

What is factor ?

Consider the expression 3ab – 5a. It has two terms 3ab and -5a. The term 3ab is a product of factors 3, a and b. The term -5a is a product of -5 and a. The coefficient of a variable is a factor or factors.

Example :

In the term 3ab;

(i) the coefficient of ab is 3 (ii) the coefficient of a is 3b

(iii) the coefficient of b is 3a.

In the term –5a the coefficient of a is –5

What is constant ?

A number which is not having any variable with it is known as constant.

Like terms (or) Similar terms :

Like terms are the terms which have the same variables with same exponent for each variable.

Examples : 

7x, 3x, - 4x

Unlike terms or Dissimilar terms: 

Unlike terms are the terms which have same variables or different variables. 

If they have same variables, the exponents will not be same. 

Examples : 

9x², 5xy, - 4xy², y, 6

Basic concept of polynomial - Examples

Example 1 :

The coefficient of x4 in -5x7 + (3/7)x4 + 3 x3 + 7x2 - 1 is

(A)  -5   (B)  -3    (C)  3/7     (D)  7

Solution :

There are five terms in the given polynomial.

The value in front of the variable x4 is know as coefficient of x4.

So coefficient of x4 is 3/7. Hence option C is correct.

Example 2 :

The coefficient of xy2 in 7x2 - 14x2 y + 14xy2 -  5 is  ______

Solution :

The value in front of the variable  xy2 is know as coefficient of  xy2.

Hence coefficient of xy2  is 14.

Example 3 :

The power of the term x3 y2 z2 is _________

Solution :

Power of x term is 3.

Power of y term is 2.

Power of z term is 2.

3 + 2 + 2  = 7

Hence the power of given term is  7.

Example 4 :

The degree of the polynomial x2 - 5x2y3 + 30x3y4- 576 xy is

Solution :

The Power of 1st term is 2.

Power of 2nd term is 5.

Power of third term is 7.

Power of fourth term is 2.

Hence the degree of the given polynomial is 7.

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ALGEBRA

Variables and constants

Writing and evaluating expressions

Solving linear equations using elimination method

Solving linear equations using substitution method

Solving linear equations using cross multiplication method

Solving one step equations

Solving quadratic equations by factoring

Solving quadratic equations by quadratic formula

Solving quadratic equations by completing square

Nature of the roots of a quadratic equations

Sum and product of the roots of a quadratic equations 

Algebraic identities

Solving absolute value equations 

Solving Absolute value inequalities

Graphing absolute value equations  

Combining like terms

Square root of polynomials 

HCF and LCM 

Remainder theorem

Synthetic division

Logarithmic problems

Simplifying radical expression

Comparing surds

Simplifying logarithmic expressions

Negative exponents rules

Scientific notations

Exponents and power

COMPETITIVE EXAMS

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Multiplication tricks

APTITUDE TESTS ONLINE

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TRANSFORMATIONS OF FUNCTIONS

Horizontal translation

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Complementary and supplementary worksheet

Complementary and supplementary word problems worksheet

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Sum of the angles in a triangle is 180 degree worksheet

Types of angles worksheet

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Distributive property of multiplication worksheet - I

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Writing and evaluating expressions worksheet

Nature of the roots of a quadratic equation worksheets

Determine if the relationship is proportional worksheet

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SOHCAHTOA

Trigonometric ratio table

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All silver tea cups

All students take calculus 

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Trigonometric ratios of some negative angles

Trigonometric ratios of 90 degree minus theta

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Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 180 degree minus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 270 degree minus theta

Trigonometric ratios of 270 degree plus theta

Trigonometric ratios of angles greater than or equal to 360 degree

Trigonometric ratios of complementary angles

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Trigonometric identities 

Problems on trigonometric identities 

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Area and perimeter

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Types of angles 

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Sum of the angle in a triangle is 180 degree

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OTHER TOPICS 

Profit and loss shortcuts

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Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6