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.