Polynomials are algebraic expressions with several terms, in which each of them is the mutiplication of some constant by some variable raised to some non negative intger. Polynomials have applications in many problems in the real world, let's discuss some of them.
Polynomials to determine how much we need to pay.
Think of this situation: You go shopping and you would like to buy some jeans, some shirts and some shoes. Suppose the price tag is nowhere around but you'd like to take the things you choose with you so you have the correct size on the way out. Since you don't know the prices yet you can asign a variable to the price of each time you choose, let's say x for the jeans, y fot the shirst and z for the shoes. Let's assume you picked 4 jeans, 5 shirst and 2 pairs of shoes, then the cost for all of them will be represented by the polynomial:
Once you know the price of each item you can plug them in the expression to determine the total price of them.
Polynomials in physics.
In physics the polynomials are a common ocurrence, for example, the distance and object falls from a certaing height h is given by the equation:
Notice how the right side of the equation is a polynomial since the height h and the accelaration a are constants; then the expression that determines the distance the object has fallen is a polynomial of second degree in t.
Another example in physics of a polynomial is the total mechanical energy of an object with mass m, this is given by the polynomial:
Since the mass of the object m, and the acceleration of the gravity g are constants this is a polynomial of the variables h (the height of the object) and the velocity v. Once we know this we can determine the total mechanical energy of the object and this will helps us to predict the future motion given some conditions.
Polynomials in economics.
Usually we can express the cost of producing an amount x of certain item with a polynomial on x. Also we can express the revenue also as a polynomial on x.
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