factor, in arithmetic, any number that divides a given number evenly, i.e., without any remainder. The factors of 12 are 1, 2, 3, 4, 6, and 12. Similarly in algebra, any one of the algebraic expressions multiplied by another to form a product is a factor of that product, e.g., a+b and a−b are factors of a2−b 2, since (a+b)(a−b)=a2−b2. In general, if r is a root of a polynomial equation f(x)=0, then (x−r) is a factor of the polynomial f(x).
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