Ancient civilizations wrote out algebraic expressions using only occasional abbreviations. These longhand notations were cumbersome. The exponent x6, for example, required notation equivalent to x · x · x · x · x · x. By medieval times Islamic mathematicians were able to talk about arbitrarily high powers of the unknown variable x, and work out the basic algebra of polynomials (although they did not yet use modern symbolism). This included the ability to multiply, divide, and find square roots of polynomials as well as knowledge of the binomial theorem, which describes how to raise a binomial to an arbitrarily high power. Persian mathematician, astronomer, and poet Omar Khayyam showed how to express roots of cubic equations using line segments obtained by intersecting conic sections, but he could not find a formula for the roots. A Latin translation of al-Khwārizmī's algebra text appeared in the 12th century. In the early 13th century, the great Italian mathematician Leonardo Fibonacci achieved a close approximation to the solution of the specific cubic equation x3 + 2x2 + cx = d. Because Fibonacci had traveled in Islamic lands, he probably used an Arabic method of successive approximations to reach his solution.
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