
is a multivariate polynomial equation over the rationals. Some but not all polynomial equations with rational coefficients have a solution that is an algebraic expression with a finite number of operations involving just those coefficients (that is, can be solved algebraically). This can be done for all such equations of degree one, two, three, or...
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http://en.wikipedia.org/wiki/Algebraic_equation

statement of the equality of two expressions formulated by applying to a set of variables the algebraic operations, namely, addition, subtraction, ... [5 related articles]
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http://www.britannica.com/eb/a-z/a/45

An equation of the form f(x)=0 where f is a polynomial. See also: Algebraic Number, Polynomial.
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https://www.encyclo.co.uk/local/20687

an equation in the form of a polynomial having a finite number of terms and equated to zero, as 2x + 4x − x + 7 = 0.
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https://www.infoplease.com/dictionary/algebraic-equation

a combination of numbers and letters equivalent to a sentence in language, e.g. y = x2 + 3x – 4
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https://www.storyofmathematics.com/glossary.html
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