Polynomials gcf Calculator

Polynomials gcf calculator is one of the interesting topics in mathematics. It is the process of performing greatest common factor for the given polynomial expression. It is the sums of a finite number of monomials are called as polynomial. Polynomial has more than one term and it has a constant value for the given each term, for that variable power of integral is raised to more than two.

Example for Polynomial expression is a2 – 26a – 28.

I like to share this help factoring polynomials with you all through my article.

Definition of Greatest common factor calculator:

Greatest common factor (gcf):

Greatest common factor is defined as the process of the highest number which divides more than two numbers or terms exactly.

Steps to find the Greatest common factor:

Step 1:

Given polynomial expression can be arranged in the order of powers

Step 2:

Each term in the given expression can be factored.

Step 3:

Find the common factors in each terms

Step 4:

Take the greatest common factor

Step 5:

Simplify the each term.

Example problem for polynomials gcf calculator:

Some example problems for polynomials gcf calculator are,

Example 1:

Find the gcf for the given Polynomial expression 3x2 – 9x

Solution:

Step 1:

3x2 – 9x

Step 2:

3 . x . x – 9 . x

Step 3:

In the given expression, common factors in the each term is 3x

3 . x . x – 3 . 3 . x

Step 4:

Take the common term outside

3x ( x – 3)

Step 5:

Solution to the given polynomial gcf is 3x (x – 3)

Example 2:

Find the gcf for the given Polynomial expression 5x2y5 – 20x4y3

Solution:

Step 1:

6x2y5 – 24x4y3

Step 2:

6 . x . x . y . y . y . y . y – 24 . x . x . x .x . y . y . y

Step 3:

In the given expression, common factors in the each term is 6x2y3

6 . x . x . y . y . y – 6 . 4 . x . x . x . x . y . y . y

Step 4:

Take the common term outside

6x2y3 ( y2 – 4x2)

Step 5:

Solution to the given polynomial gcf is 6x2y3 ( y2 – 4x2)

I am planning to write more post on Segment of a Circle and cbse sample papers for class 9 sa2. Keep checking my blog.

Example 3:

Find the gcf for the given Polynomial expression 15x3y4 – 45x5y6

Solution:

Step 1:

15x3y4 – 45x5y6

Step 2:

15 . x . x . x . y . y . y . y  – 45 . x . x . x .x . x . y . y . y . y . y . y

Step 3:

In the given expression, common factors in the each term is 15x3y4

15 . x . x . x . y . y . y . y – 15 . 3 . x . x . x . x . x . y . y . y . y . y . y

Step 4:

Take the common term outside

15x3y4 ( y – 3x2  y2)

Step 5:

Solution to the given polynomial gcf is 15x3y4( y – 3x2  y2 )

How to add Trinomials

Trinomials, a function is in the structure of ax2+bx+c =0 (where a≠0, b, c are constants). Quadratic function or quadratic equation also called  trinomials. An algebraic expression which has 3 terms known as trinomials. The product of two binomials gives a trinomial and there are two solutions for the given trinomial. To sum trinomial first it needs to combine the liked terms and then solve it. Since, the trinomial is a combination of two terms and the sum of trinomials also has three terms.

Examples problem for add trinomials:

1. Add trinomials for given function is 2x + 3y + 4z and 6x + 4y +2z.

   Solution:
   Given functions is,
    2x + 3y + 4z and 6x + 4y +2z,

Step 1:
    Write the given trinomials as,
                       = 2x + 3y + 4z + 6x + 4y +2z

Step 2:
    Then combine the terms like as,
                       = 2x + 6x + 3y + 4y + 4z + 2z

Step 3:
    Then add the given trinomials, and we get the answer,
             Answer = 8x +7y + 6z.

2. Add trinomials for given function is 8x - 2y - 9z and 3x + y +2z.

    Solution:
    Given functions is,
     8x - 2y - 9z and 3x + y +2z,

Step 1:
    Write the given trinomials as,
                       = 8x - 2y - 9z + 3x + y +2z

Step 2:
    Then combine the terms like as,
                   = 8x + 3x - 2y + y - 9z + 2z

Step 3:
    Then add the given trinomials, and we get the answer,
            Answer = 11x - y - 7z.

Examples problem for add trinomials:

3. Add trinomials for given function is 3x² + 6y² + 4z² and x² + 5y² + 6z².
    Solution:
    Given functions is,
    3x² + 6y² + 4z² and x² + 5y² + 6z²,
Step 1:
    Write the given trinomials as,
                       = 3x² + 6y² + 4z² + x² + 5y² + 6z²
Step 2:
    Then combine the terms like as,
                       = 3x² + x² + 6y² +5y² + 4z² + 6z².
Step 3:
    Then add the given trinomials, and we get the answer,
            Answer = 4x² + 11y² + 10z².

My forthcoming post is on syllabus of neet will give you more understanding about Algebra.

4. Add trinomials for given function is x + y + 4z and 6x + 4y +2z.
    Solution:
    Given functions is,
    x + y + 4z and 6x + 4y +2z,
Step 1:
    Write the given trinomials as,
                        = x + y + 4z + 6x + 4y +2z
Step 2:
    Then combine the terms like as,
                        = x + 6x + y + 4y + 4z + 2z
Step 3:
    Then add the given trinomials, and we get the answer,
             Answer = 7x + 5y + 6z.

Sine Cosine Cotangent

Sine:

          A trigonometry functions of an angle. The sine of an angle theta shortened as sin theta In a right angled triangle is the ratio of the side opposite angle to the hypotenuse. This definition applies only of angles between 0 to 90 (0 and `pi/2 ` radians).

Sin `theta` = Opposite / hypotenuse  = `(BC)/(AC)`

Looking out for more help on Sine and Cosine Identities in algebra by visiting listed websites.

Cosine:

A trigonometry function of an angle.The cosine of an angle `theta` abbreviated as cos `theta` In a right angled triangle is the ratio of the side adjacent to the hypotenuse.

Cos `theta` = Adjacent / hypotenuse = `(BC)/(AC)`

cotangent:

A trigonometry function of an angle.The cotangent of an angle `theta` ( cot  `theta` ) in a right angled triangle is the ratio of the side adjacent to it to the opposite side.
Cot `theta` = adjacent / opposite = `(BC)/(AB)`

Example problem for sin

Find the measure of the length of other sides and also find the sin function values for the given right angle triangle.

we want to find the length of side c, the hypotenuse.

Here, we know that side a has a length of 8 and side b has a length of 6.
To find the length of side c, we can use the Pythagorean Theorem which says that c²=a²+b², or
Substitute in that a=8 and b=6, we find that:

c = √ (( 8²) + (6²))

  = √ (64 + 36)

  = √ 100

c = 10 m

So the value of x is found as x = 10 m
Now we have to find the value of `theta` . we can use the sin function to find the value of `theta`
Sin `theta`     = Opposite / hypotenuse  
          = 6/10
          = 0.6
Sin `theta`  = 0.6
  `theta` = sin^-1 (0.6)
`theta`  = 37<sup>o


Algebra is widely used in day to day activities watch out for my forthcoming posts on Statistics Hypothesis Testing and Integers Number Line. I am sure they will be helpful.</sup>

Example problem for cosine, cotangent:

Find the cosine and cotangent function of the given right angled triangle.

Solution:
Here we have to find the cosine and cotangent of the given right angled triangle
Cosine`theta` = Adjacent / hypotenuse
               =  4 /  5

= 0.8

cos `theta`  = 0.8
`theta` = cos^-1 (0.8)

      = 36^o
Cotangent `theta` = adjacent / opposite =  4/3

= 1.33

cot`theta`  = 1.33
`theta` = cot^-1 (1.33)

Steps in Data Analysis

Analysis of a data is a process of inspecting, cleaning, transforming, and modeling data with the goal of highlighting useful information, suggesting conclusions, and supporting decision making. Data analysis has been the method of multiple facets and approaches, encompassing diverse techniques under a variety of names, in different business, science, and social science domains. And now we see about the steps in data analysis. (Source -Wikipedia).

I like to share this Define Quantitative Data with you all through my article. 

Two tyoes of data analysis are shown below:

• Qualitative Analysis types :

                         The reports are analyzed with the help of given data and that are supported by the qualitative Analysis    .

•  Quantitative Analysis:

                      The reports are  believed in the format of calculating types are called as the  quantitative Analysis . And it functions in the order of  normal information.
Process in data analysis types:
The some of the process in data analysis types are :

• Steps in Data cleaning:

       Data cleaning types are the is a main types for the interval of in which the data are experienced, and False  data are if important, preferable, and realistic corrected.

• Steps in Preliminary Data analysis :

       Steps in  preliminary data analysis are,

• Steps  in Quality of Data: Data can be used in a   set of  types,

         Like  Histogram, Standard possibility in plotting mean,Average variation,Median

• Steps  in Quality  analysis of size in methods:

                   The assessment of homogeneity, which provide a deference of the reliability of a component tool 

• Main steps in  data analysis:

       The main difference between of  the preliminary data analysis and the main analysis are they can get the information’s side by side.

• Types in final data analysis :

     During the final stage of  period   , the requirements  of the  of the preliminary data analysis are predictable.


Algebra is widely used in day to day activities watch out for my forthcoming posts on Simplify Using Positive Exponents and Mixed Fraction to Decimal. I am sure they will be helpful.

Example in Data analysis steps:

Example 1:
Represent the following data  in statistical histograms given below
Marks                             No.of students
0 - 5                                        2
5 - 10                                      3
10 - 15                                    4
15 - 20                                    6
20 - 25                                    2
 Solution:
Step 1: To mark the class intervals along the x – axis.
              Student marks intervals can be , 0-5, 5-10, 10-15, 15-20, and 20-25.
Step 2: To mark the frequencies along the y – axis.
               Frequencies for number of students are,4,2 , 4, 6 and 2.
               Therefore, the statistical histograms learning to depict the scale in the X-Y plane :
                                    x - axis 1 cm = 5 marks.
                                   y - axis 1 cm = 1 students
Step 3:. Total frequency = 2 + 3 + 4 + 6 + 2 = 17
           And the bar graph are drawn below:

                                

Inverse Correlation Definition

Correlation is a statistical tool which measures the degree and the direction of relationship between two or more variables.Thus correlation is a statistical device which helps us in analysing the covariation of two or more variables.

Types of Correlation

Correlation is described or classified in several different ways. Three of the most important ways of classifying correlation are:
(i) Positive or Negative(Inverse)
(ii)Simple, partial and multiple.
(iii)Linear and non-linear.

Positive and Negative Correlation.
Whether correlation is positive(direct) or negative(inverse) would depend upon the direction of change of the variables. If both the variables are varying in the same direction, i.e., if as one variable is increasing the other on an average is also increasing or, if as one variable is decreasing the other on an average is also decreasing, correlation said to be positive.If, on the other hand, the variables are varying in opposite directions, i.e., as one variable is increasing the other is decreasing or vica-versa, correlation is said to be negative(Inverse).
In other words, when two variables move in the same direction they are said to be positively correlated and when two variables moves in the opposite direction they are said to be negitively correlated.
The following examples would illustrate the difference between positive and negative correlation.

1. POSITIVE CORRELATION

X     :           10        12        15        18        20               X:          80         70         60         40         30
Y     :           15        20        22        25        37               Y:          50         45         30         20         10
2.  NEGATIVE(INVERSE) CORRELATION
X     :           20        30        40        60        80               X:         100         90         60         40         30
Y     :           40        30        22        15        10               Y:           10         20         30         40         50

Inverse correlation

My forthcoming post is on Set Builder and Interval Notation and Variable Exponents will give you more understanding about Algebra.

In a inverse correlation, as the values of one of the variables increase, the values of the second variable decrease. Likewise, as the value of one of the variables decreases, the value of the other variable increases.

This is still a correlation. It is like an “inverse” correlation. The word “negative” is a label that shows the direction of the correlation.

 Here are some other examples of negative correlations:

1. Education and years in jail—people who have more years of education tend to have fewer years in jail (or phrased as people with more years in jail tend to have fewer years of education)

2. Crying and being held—among babies, those who are held more tend to cry less (or phrased as babies who are held less tend to cry more)

Common Factoring Fractions

A common factoring fraction is the important topic in algebra.  This method is similar to taking the denominator for comparing two or more fractions.  This method is mainly used for following types of problems. They are

• Comparing fractions
• Adding fractions
• Subtracting fractions

    In this topic we have to discuss about the common factoring fractions with example problems.

I like to share this Least Common Denominator Finder with you all through my article. 

Brief explanation of common factoring fractions – Comparing Fractions

Comparing fractions:

    We can compare two or more fractions; first we can take the common denominator for all fractions. For this we can take the common factors for all denominator values. The type of comparing fractions is mostly used in the following types of problem.

They are

• Ascending order
• Descending order

Example:

Arrange the following fractions in the ascending order `(1)/(2)` , `(1)/(4)` and `(1)/(8)` 

Solution:

     Here the denominator values are 2, 4and 8. They are not equal values. So we can take common factor for all denominator values. The common denominator value is 8.

Consider `(1)/(2)` x `(4)/(4)` = `(4)/(8)`

Consider `(1)/(4)` x `(2)/(2)` = `(2)/(8)`

Consider `(1)/(8)`

     Now the denominator is same. So we can arrange the fractions in the ascending order in the following manner,`(1)/(8)`,`(2)/(8)`,`(4)/(8)`

Brief explanation of common factoring fractions – Adding and Subtracting Fractions

Adding fractions:

    We can add the two or more fractions; first we can take the common denominator for all fractions. For this we can take the common factors for all denominator values. Then we can add the numerator values.

Subtracting fractions:

    We can subtract the two or more fractions; first we can take the common denominator for all fractions. For this we can take the common factors for all denominator values. Then we can subtract the numerator values.

My forthcoming post is on Scatter Plot Graphs and Variance Math will give you more understanding about Algebra.

Example:

Simplify the fraction 1/3 + 1/6 -1/12.

Solution:

     Here the denominator values are 3, 6 and 12. They are not equal. So we can take common factor for all denominator values. That is 12.

Consider `(1)/(3)` x `(4)/(4)` =`(4)/(12)`

Consider `(1)/(6)` x `(2)/(2)` =`(2)/(12)`

Consider `(1)/(12)`

     Now the denominator is same. So we can simplify the numerator values in the following manner,

 `((4+2-1))/(12)`= `(5)/(12)`

     These are the important types of common factoring fractions.

Least Common Multiples by Prime Factorization

The unique factorization theorem says that every positive integer greater than 1 can be written in only one way as a product of prime numbers. The prime numbers can be considered as the atomic elements which, when combined together, make up a composite number. The short term for Least common multiples is LCM. (Source Wikipedia)

Examples for finding Least common multiples by prime factorization:

Example 1:

Find the least common multiples for the numbers 234 and 534 by prime factorization.

Solution:

Prime factorization for the given numbers are

234   :  2 3 3 13

534   :  2 3        89

----------------------------

LCM:  2 3 3 13 89

Least common multiples by prime factorization is 2 * 3 * 3 * 13 * 89 = 20826

Example 2:

Find the least common multiples for the numbers 584 and 564 by prime factorization.

Solution:

584    : 2 2 2 73

564    : 2 2 3 47

------------------------

LCM : 2 2 2 3 73 47

Least common multiples by prime factorization is 2 * 2 * 2 * 3 * 73 * 47 = 82344

Example 3:

Find the least common multiples for the numbers 124 and 164 by prime factorization.

Solution:

124    : 2 2 31

164    : 2 2 41

---------------------

LCM : 2 2 31 41

Least common multiples by prime factorization is 2 * 2 * 31 * 41 = 5084

Example 4:

Find the least common multiples for the numbers 48 and 58 by prime factorization.

Solution:

48      : 2 2 2 2 3

58      : 2            29

------------------------------

LCM : 2 2 2 2 3 29

Least common multiples by prime factorization is 2 * 2 * 2 * 2 * 3 * 29 = 1392

Example 5:

Find the least common multiples for the numbers 45 and 64 by prime factorization.

Solution:

45      : 5 3 3

64      :          2 2 2 2 2 2

-------------------------------------

LCM : 5 3 3 2 2 2 2 2 2

Least common multiples by prime factorization is 5 * 3 * 3 * 2 * 2 * 2 * 2 * 2 * 2= 2880

Practice problems for finding Least common multiples by prime factorization:

Problem 1:

Find the least common multiples for the numbers 56 and 456 by prime factorization.

Least common multiples by prime factorization is 3192

Problem 2:

Find the least common multiples for the numbers 64 and 65 by prime factorization.

Least common multiples by prime factorization is 4160

Problem 3:

Find the least common multiples for the numbers 560 and 4560 by prime factorization.

Least common multiples by prime factorization is 31920

Between, if you have problem on these topics Series Solutions  please browse expert math related websites for more help on Multiple Linear Regression Analysis.

Problem 4:

Find the least common multiples for the numbers 356 and 78 by prime factorization.

Least common multiples by prime factorization is 13884

Problem 5:

Find the least common multiples for the numbers 4562 and 5697 by prime factorization.

Least common multiples by prime factorization is 25989714