As we use any language to communicate, in every language, there are certain building blocks that make up the language. Polynomials, we can consider are the same as the language of mathematics as is a ‘sentence’ to the spoken or written languages. In almost all spoken languages, there are letters which when grouped together in a particular order from a word and words when put together in a specific order and as per grammar rules for sentences. Sentences then essentially block, which is then extensively used to communicate in the language of choice.
Mathematics is a language to essentially converse with the mysteries of nature. Natural patterns occurring are decoded and captured using mathematical language. Like in any spoken or written language in the language of maths, we have different symbols and numbers, and then put them together they make a polynomial which essentially defines a pattern.
Dividing polynomials we would get individual operands, these operands are grouped together along with certain operators, and we get a polynomial. For example, a polynomial like ax+by+c is the equation of a straight line, and using this polynomial we can know almost everything about this line. A polynomial like ax2 + bx + c is single-handedly responsible for knowing how to catch a ball and how to shoot a rocket in space.
Polynomials are the backbone of mathematics, and thus wherever we are using mathematics in daily life, chances are we are using polynomials. Sometimes the utility of a tool is most appreciated when it helps in generating wealth, well if that’s the case then polynomials fit the bill perfectly. As when managing finances, from calculating the time value of money or equating the expenditure with income, it all involves using polynomials.
When going from point A to point B, the curve of the path is expressed in coordinates, and the equation of the curve is used by the Maps in our phones to help us find the most optimized route, spot where we are in the map ( current location). So among so many different usages of Maps, it used polynomials underneath.
If a farmer wants to optimize how much land can be used for different crops so the profit can be optimized while some crops may have high productivity. Still, the selling price is low, and other crops may have low productivity, but the profitability is higher. In such scenarios, a polynomial is formed using constants and variables, and the maximum and minimum values of the polynomial can tell what should be the best proportion of crops.
When constructing a house, it requires extensive use of polynomials to design the structure of the house and to calculate the amount of different raw materials that will thus be required and at what rate they would be consumed, and at what rate the house would be constructed. To plan all or any part of the construction will probably require using a polynomial.
Polynomials provide information on the relation between the different terms. Each term reflects some element of nature and the constants attached to the variables define the weight assigned to the different variables. These terms then interrelate using the mathematical operators then unravel a pattern. Using the pattern in the form of a polynomial, one can forecast values. So the same polynomial can be used to create a small and a large house as the relation is the same only the magnitude has changed which in turn means by giving different values to the variables in the polynomial different results will be obtained. Still, all these results follow a familiar pattern, and this pattern is enabled by the polynomial.
The world of polynomials is further enriched by exponents, and thus we get higher forms like binomials, which essentially define how a thing when thrown a parabolic path travels. Considering we live in gravity and almost everything is thrown up following a parabolic path, it is not difficult to appreciate how useful it is to have a polynomial to capture it in one expression.