![]() ![]() Just as with rational numbers, rational functions are usually expressed in "lowest terms." For a given numerator and denominator pair, this involves finding their greatest common divisor polynomial and removing it from both the numerator and denominator. Like polynomials, rational functions play a very important role in mathematics and the sciences. Rational functions are quotients of polynomials. In such cases, the polynomial will not factor into linear polynomials. Polynomials with rational coefficients always have as many roots, in the complex plane, as their degree however, these roots are often not rational numbers. In such cases, the polynomial is said to "factor over the rationals." Factoring is a useful way to find rational roots (which correspond to linear factors) and simple roots involving square roots of integers (which correspond to quadratic factors).
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