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It is far from clear what you consider to be the six main types of polynomials, but in mathematical terms, the distinction is by the degree of the polynomial.

Degree 0: y = c. If y represents the speed of light in vacuum, then y = 299,792,458 meters per second.

Degree 1: y = ax + b. Many mobile phone tariffs work on the basis that you pay a fixed amount, b, every month for a package of allowance. When you exceed the package you pay a units of money for each extra unit. So the total cost for x extra units is y = ax + b.

Degree 2: y = ax2 + bx + c. If a simple pendulum is given a small swing then, when the displacement of the bob from the vertical is x, the acceleration is -x (in appropriate units). So y = -x2 (a = -1, b = 0, c = 0).

Degree 3: y = ax3 + bx2 + cx + d. It is easiest to give a real-world example where a = 1 and b = c = d = 0. If y represents the volume of a cube with sides of x units, then y = x3.


I cannot think of real-world examples of polynomials of degrees 4 or 5 which are not too contrived. Combinatorials will give examples, though.


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Q: What is one real-world example of each of the six main types of polynomial functions?
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