Introduction To Different Forms Of Polynomial.

 Welcome friends!

                         Today we will see different forms of polynomials. These

forms are more important for the next division methods.

                So let’s have a tour of these forms of polynomial.

Example: write the given polynomial in standard form,                                               x +3x⁵+2x³-6x⁴+4x²+1

Standard form: 3x⁵-6x⁴+2x³+4x²+x+1

Caution: while rearranging the terms you must rearrange “sign of

term, coefficient of term, variable & its exponent” together otherwise 

you may go wrong.

Index Form:

                        Sometimes in Polynomial we may come across the

polynomials which misses some power terms in between then add a 

term with coefficient zero, is called Index form of polynomial. It will be 

better to look an example.

Coefficient form of a polynomial.

                 When the coefficient of given polynomial by considering all

 the missing terms in standard form of polynomial in a bracket by

 separating commas, is called a coefficient form of polynomial.

Lets see by an example:

Another Example:

                 These forms are useful in long division & synthetic division of

 polynomial.

 

Thank you!

          Hope you understand the different form of polynomial.

You may visit also:

Algebra Index

Introduction to Division in Algebra (part 1)

Introduction to Division in Algebra (Part I)

 Welcome friends!

                         Today we learn two methods of Division in polynomial

 and different forms of polynomials.

We will two methods of division in algebra.

Method 1): Dividing each term

Let us see by an example

Let’s see some harder example:

Method 2): (By taking common terms.)         

Lets see the example

Some more…

  

Thank you!

Hope you understand the two methods of division of polynomial.

you may visit also:

Algebra Index

Introduction To Different Forms Of Polynomial.

Multiplication in Algebraic Expression (polynomial)

 

Welcome friends!

              Uptil now we have learnt about addition & subtraction of

 expression and use of exponents in algebraic expression.

              Today we are going to see the multiplication of Algebraic 

expression.

So,

        When multiplying two monomials, first multiply the coefficients along 

with the signs and then multiply the variables and their exponents if any.

Multiplication of Monomial with Monomial:

Multiplying a binomial by monomial

Steps: 1) Multiply each term in binomial by monomial.

          2) Add those answers together & simplify if necessary.

Multiplying a binomial by a binomial.

Each of the two terms in the first binomial…

                                      ….. is multiplied by …..

                      ….. each of the two terms in the second binomial.

Examples for Practice:

      1) Multiply:

i)            16xy ´ 18xy

ii)          23xy² ´ 4yz²

iii)        (12a+17b) ´ 4c

iv)        (4x+5y) ´ (9x+7y)

 

       2) A rectangle is (8x + 5) cm long and (5x + 3) broad. Find its area.

Thank you!

Hope you learn about Multiplication of Algebraic Expression (Polynomial).

You may visit this also:

Introduction to algebra ( Part I)

Introduction to Algebra (Part II)

Transposing Method of Solving Algebra

Order of Operations – BODMAS/PEMDAS

Algebra - Substitution

Introduction to Inequalities in Algebra

Introduction to Algebraic Expression.

Introduction to Addition & Subtraction of Algebraic Expression

 (Polynomial)

Degree of an Expression (Polynomial)

Use of exponents in algebra.

Algebra Index

Use of exponents in algebra.

 Welcome friends!

              Uptil now we learnt that how to Add or Subtract two or more

 Algebraic Expression. Before going for multiplication in algebraic

 expression (polynomial) we must learn the use of exponents in Algebra. 

As in multiplication we are going to multiply the variables with exponents.

What is a variable with an exponent?

• ·        Variable is a symbol for a number we don’t know yet. It is usually a letter.
• ·    An exponent says how many times to use the variable in multiplication.

What is the meaning of x⁵?

This means the x is multiplied with itself 5 times.

Here, X – Base of exponential term

         5 – Exponent / Power / Index (indicate how many times x is multiplied to itself)

In General

Benefits of using exponents

·        It is easy to read and write.

·        It is easy to calculate. (with the help of law of exponents)

Negative Exponents

Vice-versa

Means sign in exponent indicates where to move the exponent (in

 numerator or denominator) of a fraction by simply changing the sign of 

the exponent.

Positive and Negative exponents together:

Exponents of 1 and 0

Exponent of 1

When the exponent is 1, means the variable itself (x¹=x)

(Normally, we don’t write the 1 in power but it is better to remember

 that x is also X¹.)

Exponent of 0

When the exponent is 0, we are not multiplying by anything and the

 answer is just “1”. (Ex. X⁰=1, Y⁰=1, etc).

But,

Multiplying variable with exponents:

Let us see an example

Note: here, base is same & operation between them is multiplication,

 but for different base it won’t work & this is one of the laws of 

exponents.

Multiplication when mixed variable:

Let us see the example

Multiplication when having constant:

            Sometimes along with exponential variable constants appears that

 time follow the following method shown in example.

How to deal with Negative exponents

  

Dividing

We can do this by using laws of exponents

So, just subtract the exponent when division is there & the base is same.

Take some complicated examples:

Problems for Practice:

1) (2x⁴y²)(3y³)

2) (6y⁵z³)¸ (3y²z²)

3) (3a⁶b⁵)(5a²bc³)

4) (25x⁴y⁴z²) ¸ (5xy²z)

5) [(8x³y)(2xy⁶)] ¸ (4x²y³)

This is all!

Thank you!

Hope you may learn how to use exponents in multiplication here.

you may visit also:

Introduction to algebra ( Part I)

Introduction to Algebra (Part II)

Transposing Method of Solving Algebra

Order of Operations – BODMAS/PEMDAS

Algebra - Substitution

Introduction to Inequalities in Algebra

Introduction to Algebraic Expression.

Introduction to Addition & Subtraction of Algebraic Expression (Polynomial)

Degree of an Expression (Polynomial)