poly is the latin root for many
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The first polynomials went as far back as 2000 BC, with the Babylonians.
Binomials and trinomials are two types of polynomials. The first has two terms and the second has three.
To multiply TWO polynomials, you multiply each term in the first, by each term in the second. This can be justified by a repeated application of the distributive law. Two multiply more than two polynomials, you multiply the first two. Then you multiply the result with the third polynomial. If there are any more, multiply the result with the fourth polynomial, etc. Actually the polynomials can be multiplied in any order; both the communitative and associate laws apply.
Descartes did not invent polynomials.
put the variable that has the highest degree first.