Help on Polynomial Long Division

Introduction for long division of polynomials:
In this article let me help you with polynomial long division. Since i had shown you enough summary on polynomials. Let me directly help you with the following examples.

Example Problems for Study about Polynomial Long Division:
Study about polynomial long division - Example:
1) Divide 2x2 – 5x –2 by x -4
Solution:
Step 1: Given Divide 2x2 – 5x -2 by x - 4
Step 2: Take x - 3 and first two digits of given problems 2x2 – 5x
Step 3: Multiply x - 4with 2x then we can get 2x2- 8x.
Step 4: Then minus 2x2- 8x from 2x2 – 5x -1 and change the sign of 2x2- 8x before subtract the polynomial.
Step 5: Then we obtain 0 + 3x - 2
Step 6: After that x - 4 multiply with 3 then we can get 3x - 12.
Step 7: Change the sign then subtract 3x - 12 and x + 3. This could also help you on half angle formula.
Step 8: The solution is: 2x + 3 with remainder 10
2x +3
--------------
x -4) 2x2 – 5x –2

- 2x2 – 8x
----------------
0 + 3x - 2
(-) 3x -12
---------------
0 +10
---------------
Answer is: 2x + 3 with a remainder 10


I hope this exaplanation is very easy for you to understand. Keep reading may be in the next session let me help you on Examples of Mixtures

Types of Quadrilaterals

Introduction to quadrilaterals:

In this article let me explain on types of quadrilaterals. In Euclidean plane geometry, quadrilaterals are a polygon with four sides (or 'edges') and four vertices or corners. Sometimes, the term quadrangle is used, by analogy with triangle, and sometimes tetragon for consistency with pentagon (5-sided), hexagon (6-sided) and so on. The word quadrilateral is made of the words quad (meaning "four") and lateral (meaning "of sides").

Types of Quadrilaterals:

There are two types of Quadrilaterals in geometry.The following are the two types of Quadrilaterals,

* Convex quadrilaterals ( Parallelograms )

* Concave quadrilaterals.

Let us see the types of quadrilaterals briefly in the following section. This could also help us on correlation formula


I hope my information on this topic is more helpful to you in understanding this. Keep reading and leave your comments. May be in the next session let me help you on Algebraic Formulas

Help on Geometric Progression

Introduction:

In this section let me help you on geometric progression. Solving online progression is very interesting since we can find the nth term of the particular sequence in much easier way. In this article we shall learn about steps involved in progressions solving. Moreover we will see in detail about different types involved in progression.

There are three types of Progression in math,

* Arithmetic progression
* Geometric progression
* Harmonic progression

Let us see these progression and their properties in the following section.
Arithmetic Progression. This can also help us on linear programming

Definition:

It is a sequence of numbers in which each term except the first term can be calculated by adding constant number (common difference) to the immediately preceding number.

The General form of the arithmetic sequence is,

a, a+d, a+2d, a+3d………..

Here a is the first number and d is the common difference.

To find the nth term of an arithmetic progression we can use the following formula,

an=a+ (n-1) d

Properties of Arithmetic Progression:

* When we add or subtract any constant number with all the terms of the sequence, the arithmetic sequence remains an arithmetic sequence.

Keep reading may be in the next session let me help you on Polynomial Function

Note on Frequency Polygon

Introduction to Frequency Polygon:

A frequency polygon is a graphical display of a frequency table. The intervals are shown on the X-axis and the number of scores in each interval is represented by the height of a point located above the middle of the interval. The points are connected so that together with the X-axis they form a polygon

Frequency polygons are useful for comparing distributions.This is achieved by overlaying the frequency polygons drawn for different data sets. The figure below provides an example. This will also help us on kinematics equations. The data come from a task in which the goal is to move a computer mouse to a target on the screen as fast as possible. On 20 of the trials, the target was a small rectangle; on the other 20, the target

was a large rectangle. Time to reach the target was recorded on each trial.

I hope you liked my information on this. Keep reading may be in the next session let me help you on Polygon Centroid

Fundamental Theorem of Calculus

Introduction to Fundamental Theorem of Calculus :

In this section let me try to help you on fundamental theorem of calculus. Calculus originated to solve mainly two geometric problems : the first is studied by a limit process known as differentiation and the second by another limit process known as integration.

Integral calculus is the study of the definition, properties and applications of two real concepts: the indefinite integral and definite integral.

The indefinite integral is the antiderivative. the definite integral inputs a function and outputs a function a number. The technical definition of the definite integral is the limit of a sum of areas of rectangles, called Riemann sum, as propounded by Riemann. This will also help us on normal distribution table

The fundamental theorem of calculus is the statement that the two central operations of calculus, differentiation and integration, are inverse operations: if a continuous function is first integrated and then differentiated, the original function is retrieved.

Keep reading may be in the next session let me help you on Polynomial Function.

Definite Integral Calculator

Definite integral calculus:

Definite integral calculator is same as the integral calculus calculator but it is mainly for finding the integral which is covered by a specific intervals. That is it has upper limit value and lower limit value.

For this definite integral calculus calculator first the given expression should be integrated as integral calculator and then the limits should be applied. The final output can be derived by substituting the upper limit – lower limit.

Integral calculator:

Integral calculus calculator is mainly for finding the indefinite integral of the given expression by getting an input value.

Consider an expression x then the integral calculus gives the calculator is, This will also help us on integral table

Example:

Find the integral calculus calculator of the function f=10x3.

Solution:

Given,

Function f=10x3

We know the integration of xn is

Therefore [int 10x^3] =10 [intx^3] =10 [x^4/4]

= [5/2x^4]

Keep reading may be in the next session let me help you on Linear Definition

Sample Problems on Radicals

Introduction for radical:

The opposite operation to the exponent is known as radical. A radical is an expression which contains the square roots, cube roots etc. For example the expression √49 can also be called as square root of 49 or root of 49. Radicals have the same property of the numbers.

Examples for Radical:

Following are the examples of radicals.

Example 1 for radical problem:

Simplify the radical: √ (49) / (√36)

Step 1: Factors of 49 = 7 × 7

√ (49) = √ (7 × 7)

= √7²

Step 2: Square root of 7² = 49

Step 3: Factors of 36 = 6 × 6

√ (36) = √ (6 × 6) = √6²

Step 4: √6² = 6

Step 5: so, √ (49) / √36) = 7 / 6

The answer of the given radical is 7 / 6

Even Rules of Radicals helps us understand better in doing all the problems.

Example 2 for Radical Problem:

Simplify the radical: 3√8 × √12

Step 1: Find the factor of 8 = 2 × 2 × 2

Step 2: Take cubic root of 8 = 2

Step 3: Find the factor for 12 = 2 × 2 × 3

Step 4: Take square root of 12 = 2 √3

Step 5: so, 3√8 × √12 = 2 × 2 √3

The answer for the given radical is = 4√3

This was just a sample examples on this topic. keep reading and leaver your comments. if you like this. May be in the next session lets study on dividing radicals

Help on Probability

In this lesson let me share with you on what is probability and its importance to mathematics.

Introduction to Probability:

In our day to day life, we come across many uncertainties of events. We wake up in the morning and check the weather report. The statement could be 'there is 60% chance of rain today'. This statement infers that the chance of rain is more than that having a dry weather. We decide upon our breakfast from a statement that "corn flakes might reduce cholesterol". What is the chance of getting a flat type on the way to an important apartment? And so on.

How probable an event is? We generally infer by repeated observation of such events in long term patterns.

Probability is the branch of mathematics devoted to the study of such events and this study also will help us on probability problems.

I hope you enjoyed reading this. Keep reading and leave your comments. May be in the next lesson let us study on Probability Calculator.

Note on Trigonometry Fuctions

Studying about trigonometry is always interesting since it contains major parts of math factions in it. Before we go more deeply on Trigonometry Functions.. Let me show you what is trigonometry.

What is Trigonometry:-

Trigonometry is noun, trigonometric is adjective: the first part of the word from Greek trigon"triangle". The second part of the trigonometry is from Greek Merton "a measure." The Indo-European root is probably me- "to measure." trigonometry is the literally the measuring (of angles and sides) of triangles. Historically speaking, the triangular approach to trigonometry is ancient where’s the circular approach now taught in our schools is relatively recent

Applications of Trigonometry:-

There are enormous number of uses of the trigonometry and trigonometric functions. For instance of the technique of triangulation is used in astronomy to measure the distance to nearby stars, in geography to measure distances between landmarks, and in satellite navigation systems. The sine and cosine functions are the fundamental to the theory of periodic functions such as those that describe sound and light waves

Trigonometric Functions:-

A common use of the mnemonics is remember facts and relationships in trigonometry

For example, the sine, cosine, and tangent ratios is a right triangle can be remembered by representing them as strings of letters, as in SOH-CAH-TOA.

Sine = Opposite ÷ Hypotenuse

Cosine = Adjacent ÷ Hypotenuse

Tangent = Opposite ÷ Adjacent

The memorization of this mnemonic can be aided by expanding into a phrase such as "SomeOfficers Have Curly Auburn Hair Till Old Age" Any memorable phrase constructed of words beginning with the letters S-O-H-C-A-H-T-O-A will serve.

I hope my information on this topic was more helpful to you.. keep reading and leave your comments..

How do Solve Proportions

Before we learn about how to solve proportions.. let me help you go through cross multiplication to solve proportion. this will help you understand better about proportion..

A proportion is an equation which states that two ratios are equal.

When the terms of a proportion are cross multiplied, the cross products are equal.

Cross multiplication is the multiplication of the numerator of the first ratio by the denominator of the second ratio and the multiplication of the denominator of the first ratio by the numerator of the second ratio.

    21      3     --  =  --            70     10     21 * 10 = 70 * 3       210 = 210 

If one term of a proportion is not known, cross multiplication can be used to find the value of that term.

     x      3     --  =  --            70     10     x * 10 = 70 * 3       10x = 210            10x   210     --- = ---     10    10            x = 21 

This was just a sample problems on proportion.... keep reading and leave your valuable comments .. may be in the next lesson.. let me help you go through deeply on Algebra , number system, and matrix. I feel these are the major and simple topic which we need to know before we learn anything about math,,, Keep reading and leave your valuable comments... to help you better.

Types of Matrices

What is Matrics?

A matrix is an arrangement of items into labeled rows and columns within a table.

It shows the relationship between two categories of features that are relevant to the items in the matrix. The row headings represent features belonging to one category. The column headings represent features belonging to another category.

Types of Matrices:- Following are the types of Matrices

• Column matrix
• Row matrix
• Square matrix
• Diagonal matrix
• Scalar matrix
• Identity matrix
• Zero matrix

7th grade math equations

7th grade math equations are the basic introduction for students for quadratic equations.

An equation is a mathematical statement, in symbols, that two things are exactly the same (or equivalent). Equations are written with an equal sign, as in the following problem

This algebra tutoring problem explain you more clearly about ,how to form an equation and get the answer for word problems.

Question:-

john traveled 234 miles in 14 days.His trip is for 42 days .Find the number of miles that he can travel in 42 days.


Answer:-

Miles:-  234    x


Days:-   14    42

Unknown quantity is taken as x.

Let's use a technique of cross multiplication from multiplication.com
By cross multiplication,we get

14 x = 234*42

divide by 14 on both sides

we get x=702

So john will travel 702 miles in total 42 days.

Find the mid point between 2 points

Topic :- Midpoint of 2 points

The midpoint between two points whose coordinates are known will be found. We will also develop a general formula for determining the coordinates of the midpoint and go through an example.
This math help explains ,how to find the midpoint.

Question:

Find the mid-point between

(2,2)and (6,4)

Answer:-

midpoint formula
to points is

  x1+x2          y1+y2
x= -------- , y = -------
    2              2

So ,Let's say.

 ( 2 , 2)   ( 6 , 4 )
   x1  y1     x2  y2


Then the mid point is

       2+6        2+4
   x= ----- , y= ------
        2          2

        8      6
     = ---  , ----
        2       2

     =  4 , 3

So the mid point is (4,3)

For more help on this ,you can reply me .