Informally, the greatest common divisor (GCD) of two polynomials and is the largest polynomial that divides both and evenly. The definition is modeled on the concept of the greatest common divisor of two integers, the greatest integer that divides both. For polynomials, the situation is slightly more complicated, because there is no canonical order which we can use to say which polynomial is "biggest.
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Greatest common divisor
In mathematics, the greatest common divisor (gcd), also known as the greatest common factor (gcf), or highest common factor (hcf), of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder. For example, the GCD of 8 and 12 is 4. This notion can be extended to polynomials, see greatest common divisor of two polynomials.
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Polynomial
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents. For example, x ¿ x/4 + 7 is a polynomial, but x ¿ 4/x + 7x is not, because its second term involves division by the variable x (4/x), and also because its third term contains an exponent that is not an integer (3/2).
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