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  Polynomials (Greek, ‘many powers’) are among the most fundamental of mathematical objects. Their use originated with the need to solve equations involving powers of numbers (the number multiplied by itself n times is the nth power of the number in question). A polynomial (in one variable) is the sum of multiples of powers of the unknown (usually written x), such as 4x5 + 3x2 + x + 2 (they are usually written with the powers decreasing, for clarity). The ‘degree’ of the polynomial is the number of the largest power involved in it: 5 in the above example. The smaller degrees have special names: 1 is linear, 2 quadratic, 3 cubic, 4 quartic and 5 quintic. The study of solutions of this kind of polynomial is the inspiration of Galois theory.

It is also possible to have polynomials with more than one variable: for example, xy3 + 3x2y + 5 has two variables, x and y, and degree 4 (because xy3 is a multiple of a term with degree 1 (x) by a term with degree 3 (y3), and you add these together). SMcL



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