Solving Polynomials

What are Polynomials?
The simple definition of Polynomial is that, it is an expression containing multiple terms that are combined together through addition, subtraction and multiplication. This polynomial definition is illustrated by this polynomial equation: 3x + 4y + 5. In this example, the polynomial equation is a combination of three terms.

Ways of Solving Polynomials
There are different ways of solving polynomials and the strategy differs based on the polynomial equation provided. In this article, let us discuss two different ways to solve polynomial through relevant examples.

Example 1: Solve polynomial (a+8) (2a-10)

In this equation, there are two sets of terms that are multiplied with each other. To solve this polynomial, multiply each term of the first set with all the terms in the second set. This is illustrated below:

When ‘a’ is multiplied with ‘2a’, it gives 2a2. Then ‘a’ is multiplied with -10, which results in ‘-10a’. As a next step, multiply 8 with the terms in the second set. When ‘+8’ is multiplied with ‘2a’, it gives ‘+16a’ and ‘+8’ multiplied with ‘-10’ gives ‘-80’. Now the equation is dissolved into:

(a+8) (2a-10) = 2a2 -10a + 16a -80

In the above equation, the second term (-10a) and the third term (+16a) contains the same term with the same degree, but the constant value alone varies. When there are several terms with same variable and same degree, they can be combined. In this case, -10a+16a can be rearranged as 16a-10a, which when solved results in 6a. Thus, the polynomial equation is further solved into the result 2a2 + 6a – 80.

Example 2: Solve polynomial equation a+2b = 5a+7b
In this equation, there are two polynomials, one on the left hand side and the other on the right hand side. In this case, these polynomials help each other to find the solution. The polynomial solver for this expression will be evolved through the steps below:
• Original Expression: a+2b = 5a+7b
• Moving right hand side expression to left: a +2b-5a-7b=0.
• Grouping terms of same variables and degree: a-5a+2b-7b=0
• Combining terms of same variables and degree: -4a-5b
• Take common factor out: -1(4a+5b)

Thus the result is -1(4a+5b).

When the polynomials are complex, the above strategies alone might not work. For instance, if you are solving quadratic polynomials then you have to perform series of steps such as finding zeros of the polynomial, finding roots and much more to solve them.

What is a Perfect Number?

A Perfect Number is nothing but a whole number, which is identical to the sum of its each and every proper divisor.

Perfect numbers

What are Divisors?
Divisors are same as the factors of a number.  A divisor or factor is a number which divides a number evenly and gives the remainder as zero. Finding factors of a number is simple. For example, consider the number 9.  The divisors or factors of 9 are 1, 3, 9, because only these three numbers can divide 9 without leaving any remainder.

Mathematical problems are solved by finding factors and multiples as we did now. In the above case, 3 is the factor of 9 as it divides 9 evenly. At the same time, 9 is a multiple of 3 because 3 X 3 = 9. This signifies that finding factors and multiples are necessary to find the perfect numbers and to solve many algebraic expressions.

What are Proper Divisors?
Proper divisors are the divisors of the number excluding the number itself. As already discussed, the divisors or factors of 9 are 1, 3 and 9. The proper divisors of number 9 are 1, 3, and 9. Number 9 is not a proper divisor of 9 because it is the same as the original number for which the divisors are identified.

What are Perfect Numbers?
Knowing what proper divisors are, now let us look at the question: What is a perfect numbers? Identify the proper divisors of a number and add them. If the result of addition is same as the actual number for which the divisors are identified, then that number is a perfect number.

For example, we identified 1 and 3 as proper divisors of9. Now add these proper divisors:
1 + 3 = 4

Here the sum is 4. Instead, if the sum was 9 (the actual number for which you found the divisors), then 9 will be called as perfect number. In this case, sum is 4 and not 9. This signifies that 9 is not a perfect number.

Let us take up another example. Are 6 a perfect number? The divisors or factors of 6 are 1, 2, 3, and 6. The proper divisors of number 6 will then be 1, 2 and 3. Now, add these proper divisors.  Addition of 1, 2 and 3 will result in 6. The result 6 is same as the number 6 for which we identified these proper divisors. Thus, 6 is a perfect number.

The other perfect numbers are:
• 28
• 496
• 8128

Applied Statistics learning

Let's learn about what is applied statistics in today's post.

Applied statistics is that section of statistics which can be applied in real life. There are different levels of measurements and these are:

• Nominal measurement
• Ordinal measurement
• Ratio measurement
• Interval measurement

Next time will help you learning on examples of analyzing data.

You can also avail to a math tutor for more help. On can also get help for other subjects such as biology tutoring and so on.

Do post your comments.

8th grade math problems

In this blog we will learn about 8th grade math problems,we can see one example problem of 8th grade math problems given below:
Solve: 16(s – 4) – 26s - 21 = 9(s + 8)

Solution:

Given expression is,

16(s – 4) – 26s - 21 = 9(s + 8)

Multiplying the integer terms

16s - 64 – 26s - 21 = 9s + 72

Grouping the above terms

-10s - 85 = 9s + 72

Add 8 on both sides

-10s + 85 – 85 = 9s + 72 + 85

Grouping the above terms

-10s = 9s + 157

Subtract 9s by on both sides

-10s – 9s = 9s + 157 – 9s

Grouping the above terms

-19s = 157

Divide -4 on both sides

s = -157/19

Answer: s = -157/19.Next we will learn about an grade 6 math probability example.Suppose the rectangle is divided into 4 parts, 2 parts of the rectangle are colored as pink ,one part of the rectangle is divided as blue and the one part is colored as yellow find the probability of the blue region ?

Solution:

Here the rectangle is divided into 4 parts so it is the total number it will be represents in the denominator and only one part is colored as blue region it will be represents in the numerator so the probability of the blue region will be shown as below ,

¼=0.25In the next blog we will learn about standard form,hope you like the example of 8th grade math problems,please leave your comments if you have any doubts.

collinear points

In this blog we will learn about collinear points.Collinear points are the points that lie on the assonant distinction whereas the non-collinear points do not lie on the assonant pipe.The erect blood can ever be haggard finished two points, so the two points are always collinear.A credit, on which points lie, specifically if it is akin to a geometric amount much as a triangle, is sometimes titled an alinement.We can use interval expression to chance out whether the relinquished ternary points are collinear or not.We will now see one example of square inch calculator,

1. Convert the area of 2.2 sq yards into square inches using calculator.

Solution:

1 square yard = 1296 square inches.

2.2 square yard = 2.2 *1296 square inches

2.2 square yard = 2851.2 square inches

2. Find the area of 3 square foot in terms of square inches.

Solution:

1 square inch = 0.006944 square foot.

1 square foot = square inches

3 square foot = square inches.

= 432 square inches.

3. convert the area of 25 square centimeters into square inches.In the next blog we will learn about statistics.Hope you like the above example of collinear points,please leave your comments if you have any doubts.

examples of probability

In this blog we will learn about examples of probability,we can one one example of probability given below.

If there are 6 apples, 3 oranges, and 1 banana in a basket, what is the probability of choosing an apple without looking in the basket?

Solution for example of probability:

P(choosing an apple)= 6/10 = 3/5 = 0.6 = 60%

The numerator is 6 because there are 6 apples in the basket, therefore six outcomes. the total number of outcomes = 10.Next we will learn about dividing polynomials calculator,we can see one example here:

Solve divide polynomial

Solution:-

Given :

= -

=

Explanation:-

First to separate the equation by denominator then divide both sides equation. Finally we got an answer as .In the blog we will learn about area of circle.Hope you like the above example of examples of probability,please leave your comments if you have any doubts.

square root of 15

We can learn about square root of 15, and we can do this with the help of an example.

The example problems based on square root of 15 is given below that,

Example 1:

Calculate the square root of 15.

Solution:

Step 1:

Here, square root of 15 is nearly equal values between 3² and 4². Because 3² = 9 and 4² = 16.

Step 2:

So, now divide 15 by minimum square value of 3.

Step 3:

Now, take the average value for 5 and 3.

Step 4:

Now, divide 15 by 4

Step 5:

Now, take the average value for 3.75 and 4.

In the coming blog we will learn about surface of a rectangle and integers.Please leave your comments if you have any doubts.