Polynomials: A Brief Description

In order to understand mathematics, first, you have to speak the language. The problem is, with mathematics, unlike French or German or any other spoken language, this dialect is replete with difficulty and at times quite incomprehensible. And in mathematics, even when you understand something, you still often feel as though you really need to understand it even more. Thus, it certainly helps if you can get off to a good start by at least understanding some of the languages. Here we give insight into what a polynomial is and then we will continue their operations like multiplying polynomials, adding, subtracting them.

Multiplying Polynomials
Multiplying Polynomials

A polynomial is an expression found in algebra. Technically a polynomial of degree n is an expression of the form a(n)x^n + a(n-1)x^(n-1) +… + a(1)x + a(0), where each of the a(n) terms corresponds to some integer, the n-terms following the x^ correspond to the exponents and are positive integers, and n and a(n) are not equal to 0 (if they were then this would not be a polynomial of degree n). In plain English, a polynomial is any expression such as 3x^4 + 2x^3 – x + 4, or 2x^2 – 3x + 1. The degree is the highest exponent that occurs in the expression. Thus, the first polynomial is of degree 4 and the second is of degree 2.

The first few polynomials, those of degree 1, 2, 3, 4 and 5 have special names. A first-degree polynomial is a linear function because its graph produces a line. The second, a quadratic; the third a cubic; the fourth a quartic; and the fifth, a quantic. After these, the polynomial is generally referred to by its degree.

The above-written polynomial uses the variable x, and this is most common; however, we could just as easily have written a polynomial in some other letter or variable, and some common other choices would be the letters y or t. Bear in mind that changing the letter in which the polynomial is written does not alter the nature or behaviour in any way.

Polynomials are just one kind of algebraic expression. They are very useful in modelling many real-world problems, and they occur in many formulas. In more advanced courses, polynomials are encountered to serve as substitutes for other functions for which no apparent similarity is evident. Thus, the amazing versatility of polynomials. Multiplying polynomials is very easy, and you should be knowing how to do the same. Otherwise, you will not be able to solve any algebraic problems.

As far as the pictures, or graphs, of polynomial functions, they look somewhat like roller coasters, often with many hills and valleys. These curves are “smooth” in the sense that they have no sharp turns or corners and can be drawn all in one piece. For this reason, these polynomial functions play an important role in the branch of mathematics called analysis and serve as an important tool in many other branches as well. So, do learn the world of polynomial and conquer the mathematics.

Finding the Greatest Common Factor GCD with Quickmath Calculator

The greatest common factor, commonly just indicated as GCD, refers to the largest number that can divide more than two integers without a remainder. The main condition is that neither of the two or more numbers be zero. Someone may wonder what it would actually help in real life, to struggle in the attempt of find a greatest common divisor. Some of its real life applications include cryptography and even more practical uses like sharing and distribution of profits.

online math problem solver
Online Math Solver

Finding GCD

When manually finding the GCD of a particular set of numbers, you will be required to start with the lowest common factor first. For example, if you have a set of five numbers, 2, 6, 8, 10, and 12; you will first have to start with the lowest possible factor, which can divide all these numbers without leaving a remainder. 1 is the number in that case. But 1 will always divide all numbers, so it usually is excluded in the list of possible greatest common factors, unless it happens that no other greater number can be settled on as the single greatest common divisor. Like in the set of numbers in our example, both 1 and 2 can divide all the numbers without leaving a remainder. But 2 is greater than 1, so 2 will be the GCD. Note that here we have picked on a very simple case for convenience. When it comes to very large numbers and decimals, the case actually gets beyond manual manipulation abilities.

Using Quickmath Calculator to find GCD

What happens in the background of the Quickmath Calculator is that it actually breaks each number into respective common factors. It represents all numbers in a set of their smaller expressed multiples. When all the factors have been identified, the largest of the common ones is selected and returned as a result. With Quickmath Calculator, you can actually get to follow the whole process of finding the factors and comparing them to come up with the needed GCD. What you need to do is visit Quickmath.Com. A homepage will work with an online model of a calculator in the display. For finding GCD, you will be required to select the factor option on the side bar. Enter the number you want to find independent numbers you want to find GCD for. After that, click on the factor button. The factors of the number will be displayed as the results. When you have repeated the process for the individual numbers you are looking for GCD for, then you can compare the results, and easily pick on the required GCD.  There are also the particular steps which have been followed, to come with the particular individual results. In any case that you are interested in following the individual steps one by one, Quickmath Calculator gives you that chance. You can also try as many complex numbers, to see the reality of how Quickmath Calculator works in finding GCD.

Students’ Common Errors in Working with Fractions

When teaching Fractions, teachers should be watchful for students’ basic misguided judgments that prompt to mistakes in calculation.

Trusting that portion’ numerators and denominators can be dealt with as entire independent numbers.

Students who like adding or subtracting fractions the numerators and denominators of two parts, for instance, 2/4 + 5/4 = 7/8. The students neglect to perceive the relationship between the denominator, i.e. that the denominator is the quantity of equivalent amounts of into which one entire is partitioned and that the numerator implies the number of those parts. The way that numerators and denominators are regarded as entire numbers in augmentation just adds to the perplexity.

Subtracting Fractions
Subtracting Fractions

To conquer this misinterpretation, display a genuine issue. Ask students a question this way: “if you have 3/4 of an orange as well as give 1/3 of it to a companion, what division of the first orange do you have left?” Subtracting the numerators and denominators independently would bring about a reply of 2/1 or 2. Students ought to instantly perceive that it is difficult, to begin with 3/4 of an orange, give some of it away, and wind up with two oranges. Such cases help students see why regarding numerators and denominators as isolated entire numbers are improper and will make them more responsive to a fitting methodology.

If you fail to locate a shared factor while Adding or subtracting fractions with not at all like denominators.

Students frequently neglect to change over portions to a common, proportional denominator before adding or subtracting them, and rather only utilize the bigger of the two denominators in the reply (e.g., 4/5 + 4/10=8/10). Students don’t comprehend that diverse denominators reflect distinctively measured unit divisions and that adding and subtracting parts requires a typical unit portion (i.e. denominator).

The same basic confusion can lead students to make a similar mistake: Changing the denominator of a portion without rolling out a relating improvement to the numerator—for instance, changing over the issue 2/3 + 2/6 to 2/6 + 2/6. Number lines as well as other visual representations that show proportionate portions are extremely useful.

They believe that lone entire numbers should be added or subtracted with a fraction.

While adding or Subtracting Fractions, there is a high probability that students may disregard the partial parts, and work just with the entire numbers. Students either work on an issue they don’t comprehend, a misconception the significance of blended numbers or expecting that such issues essentially have no arrangement.

A related misguided judgment is feeling that entire numbers have an indistinguishable denominator from a part of the issue. This misinterpretation may lead students to decipher the issue 4 – 3/8 into 4/8 – 3/8 and discover a reply of 1/8. At the point when given a blended number, students with such a misguided judgment may add the entire number to the numerator, like (3/3 + 1/3) × 6/7 = 4/3 × 6/7 = 24/21.

Leaving the denominator unaltered in part expansion and augmentation issues. Students regularly exit the denominator unaltered on part duplication issues that have to break even with denominators (for instance, 2/3 × 1/3 = 2/3). It may happen because students experience more portion expansion issues than division increase issues. They mistakenly apply the right system for managing measure up to denominators on expansion issues to duplication.

Solve For X with QuickMath Calculator

Alphabetic letters are frequently used in mathematical expressions to represent variable values. A variable value means a value that can keep changing as per the preferred results. The letter x is the most used letter when it comes to representing variables.

Solve for X
Solve for X

How to Solve for X Quickmath Calculator

QuickMath calculator can be used to solve for x in various fields. From graphical equations, inequalities to algebraic equations;

Algebra

Algebraic expressions may require you to expand, factor, simplify or cancel out. When solving for x in algebraic expressions, there will be no equating, so the real values of x cannot be gotten. Algebraic expressions have no equal signs, and only aim at simplifying and representing an equation as simple as possible. Quickmath Calculator can be used to solve for x in all algebraic expressions and commands. Note that here; the value for x will likely be the simplest form in which that particular equation can be represented in. This is brought up by the fact that algebraic expressions do not have real equating values.

Equations

Almost all equations that can be solved using Quickmath Calculator will have x as the variable. All that is needed with the Quickmath Calculator is to enter the exact equation as it is written in the question paper or the particular sources for particular cases. Here, make sure you have chosen in the correct category of the expression or equation you have on the side bar of www.quickmath.com home page.  When you click on the solve button, you will have the results displayed on the real or approximate values of x. Most equations will also require you to plot the related graph. This is still part of solving for x. Since you can have graphs easily plotted for you with QuickMath calculator, the value for x will be the points at which the plotted graphs touch the x-intercepts.

Inequalities

Whenever you get to run an inequality on the QuickMath calculator, the results will be displayed indicating the real or approximate values for x. Inequalities require that the variables, in our case x, be represented on the left side of the equation. Therefore, the right side of the entered equation will be the value for x.

Advantages of using QuickMath calculator to Solve for X

QuickMath calculator returns instantaneous results. It also does not necessarily require a user first to download and install the calculator. All the operations can be done online. The calculator also displays all the steps followed in the process of solving for x. Users can also run as many expressions and equations as needed. All will have the specific value of my solved and displayed in the results. For graphical plotting, the value of x will be easily accessed by picking the real values where the plotted graph crosses the x-intercepts.

The Basic of Multiplication

Multiplication denoted with juxtaposition, cross sign or asterisk.  It is among the four elementary, arithmetic and mathematical operations while others are division, subtraction, and addition. Multiplying is a repeated addition while a multiplication of two different numbers will be adding copies of one of the two.  One is said to be multiplicand which is the first value while the one is called multiplier.  A multiplier is the one that it is written for the first time while the multiplicand is in the second position. The multiplication of the integers will include some negative numbers while the rational numbers like fractions or real numbers will be defined using a systematic generation for the basic definition.  The multiplication may be visualized while counting the objects that are arranged into the rectangle for an entire whole number or to find an area of a rectangle where the sides are given a certain length.  An area of the rectangle will not be based on the side that had been measured before the other, and this is how it illustrates commutative property. A product of two measurements will be new types of the measurement. The example is that when you multiply two sides for a rectangle, it will give a dimensional analysis.

Multiplication
Multiplication

An inverse of multiplying is dividing. The example is that 4 by 3 equals to 12 while 12 divided by 4 equals 3. Multiplication may also be defined using different numbers like complex numbers or abstract constructs like matrices.  The order for which the matrices have to be multiplied in will not matter.  There is a listing of different types of products which are being used in mathematics.

In arithmetic, a sign of multiplication is X found between two terms. Multiplication may also be showed by a dot sign. With algebra, the multiplication that involves variable will be written through juxtaposition. This notation may also be used for the quantities which are found within parentheses.  These types of multiplication may lead to ambiguity if the concatenated variable takes place for matching a name of a new variable.

With matrix multiplication, you should know that there is a distinction between a dot symbol and a cross. A cross symbol means taking the cross products for two vectors and it leads to a vector. A dot is used to denote a dot product for two vectors, and this may lead to a scalar.

In the computer programming, an asterisk is a common notation. This is because at the beginning, the computers had limited number of small characters and there was no multiplication sign and asterisk was on each keyboard.

A common method used to multiply simple numbers using paper or pencil requires the use of the multiplication table and it has to be consulted or memorized for small numbers.  Multiplying numbers with decimal places; can be error prone and tedious.  The common logarithms had been invented to be used for these calculations. Multiplication has now become easy by the use of electronic computers and the latest calculators which reduce the need to multiply manually.

Solution to your Algebra Problems

Are you fond with numbers and variables?

How about equations?

Math problem solving?

Algebra?

If you answered yes to all of these questions then I guess you landed on the wrong read about. But I’m guessing that the reason you’re still continually reading is because you answered No to even just one of the questions above.

Algebra Solution
Algebra Solution

Most of us claim that they hate math, but in reality they don’t really mean that. What they actually meant was I’m confused with math and I don’t want to spend another minute figuring out what to do next. This is very true especially when it comes to algebra. Since algebra is the connecting link of all the field of mathematics, just like the road systems, making it so broad, complicated and confusing? It touches and involves everything that is related to math.

There’s a study that says, when a person is confused, he or she stops. It’s the average of the norms. That’s why a lot of people especially students don’t finish solving math problems, not to mention long and complicated algebraic expressions. Until, they find a valid reason of spending too much time enduring the headache these math problems, they will not do it.

But you say that this is part of living, and studying of course. Yes that’s right and the only way to make us and the students to love solving algebraic expression is by making them want it. So how do we do that?

First, let’s identify the root cause of why they don’t like to do it? Well, because it’s complicated, takes too much time and doesn’t provide checking or verifying solutions. The same reason why it becomes so frustrating coming up to a wrong answer when you thought you were doing right all along. Then what’s next? Repeat the whole process, solve the equation and hope that this time you make it right.

Now that we’ve identified the cause, what’s the solution? Well first, as adults we have to remember that we’re already living a complicated life and as students we are already having a hard time figuring out a way to pass all of our subjects. Then why not just make life easier but looking for solutions the fast way. The internet is making a great job dealing with these fast and easy solutions.

And for our math problems we have what we call the math solver. Here, you can come up with answers the simplest possible way. Just by entering the equation in the solver then it almost automatically gives you the answer. In that way, all we have to worry about is the analysis of the problem with the given solution. Easy and simple, isn’t it? No need to recomputed and end up with the same wrong answer. We can even learn techniques on how to solve similar problem. I’m sure a lot more will be encouraged to finish up solving math problems when we know that it is this easy and there’s a way to verify our results.

math calculator

Make Math Calculator Your Best Friend

Math may not be everyone’s friend. You may be one of those who are finding it hard to come up with answers while the others are very natural with it. If that is the case with you, you must immediately take the help of the math calculator. This is a great way of deriving answers to various types of questions that one may come across in arithmetic and other branches of math.

Importance of math in day to day life

Math is an essential subject for understanding the very concept of life. When you are dealing with life on a day to day basis, you need to measure various aspects of it so that your life goes on smoothly. If you are not able to make calculations about how much ingredient goes into a dish or how much change you need to give to the vendor after you have bought a certain thing from him, then it may become really difficult for you to survive. This is why all the elementary, as well as primary schools, have included math as an essential subject in their academic curriculum. Math makes it easy to understand and explain various aspects of not only the academic curriculum but also the extracurricular activities like sports, art, etc. thus you see that math has importance for all and in all walks of life without any doubt and studying math is as essential as living itself.

Why some people find it difficult?

Many people do not like t solve math because it takes a certain part of our brain to function and not many have that part trained to do so. To be able to solve the problems of math, it is important that you have a good teacher who can help you whenever you are stuck. You may have a good teacher in school, but that does not mean that you can take their help at any time. You will have t wait till you meet the teacher and ask your problem and this is where math calculator comes to your rescue.

What all can you do with math calculator?

Math calculator that is available online is a great tool for all students as they can access the calculator at all the times and any place because it is now available even for the mobile and tablets. This tool helps you to solve your math problem in just a few seconds time. You need not fret that you have no one to help at home; you can just open your browser, select the best online math calculator, put in your problem and get the answer. It is just not the answer that you get; you even get the detailed step by step explanation of whatever type of problem you are having the problem with.

The main aim of a student is to get their problem solved and if the help is so easily available there could be nothing better than that.