Although many of us don't realize it, people in all sorts of professions use polynomials every day. The most obvious of these are mathematicians, but they can also be used in fields ranging from construction to meteorology. Although polynomials offer limited information, they can be used in more sophisticated analyses to retrieve more data.
What is a Polynomial?
Polynomials are algebraic expressions that add constants and variables. Coefficients multiply the variables, which are raised to various powers by non-negative integer exponents.
How to Solve a Polynomial
These equations are solved by finding for the variable. Polynomials come in varying degrees, some of which are solved by particular equations. Factoring, rational equations and root extractions can solve those in the lowest four orders. For example, second-order equations (of the form f(x) = ax^2 + bx + c) can be solved by the quadratic equation (ax^2 + bx +c = 0). Third-order equations are solved by the cubic equation and fourth-order equations are solved by the quartic equation.
How do People use Polynomials?
Since polynomials are used to describe curves of various types, people use them in the real world to graph curves. For example, roller coaster designers may use polynomials to describe the curves in their rides. Combinations of polynomial functions are sometimes used in economics to do cost analyses, for example.
Polynomials for Modeling or Physics
Polynomials can also be used to model different situations, like in the stock market to see how prices will vary over time. Business people also use polynomials to model markets, as in to see how raising the price of a good will affect its sales. Additionally, polynomials are used in physics to describe the trajectory of projectiles. Polynomial integrals (the sums of many polynomials) can be used to express energy, inertia and voltage difference, to name a few applications.
Polynomials in Industry
For people who work in industries that deal with physical phenomena or modeling situations for the future, polynomials come in handy every day. These include everyone from engineers to businessmen. For the rest of us, they are less apparent but we still probably use them to predict how changing one factor in our lives may affect another--without even realizing it.