How to Do Long Division With Rational Functions
A rational function or expression is a ratio of polynomials. In simpler terms, it is a fraction with a polynomial in the numerator and denominator. Polynomials are expressions that contain variables, numbers and positive whole number exponents. Knowing the terms describing the parts of division makes long division easier to perform. The divisor is the number/polynomial being divided into another number/polynomial, which is called the dividend.
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Instructions
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Practice solving polynomial long division using the rational function (x^2 - 6x - 8) / (x + 1). Write the dividend, x^2 - 6x - 8, inside the long division bracket. Write the divisor, x + 1, to the left of the bracket.
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Divide the first term of the dividend, x^2, by the first term of the divisor, x: x^2 / x = x. Write "x" in the first answer slot on top of the bracket. Multiply this "x" to the remaining term of the divisor: 1 * x = 1x. Write the newly formed expression x^2 + 1x below the first two terms of the dividend and subtract: (x^2 - 6x) - (x^2 + 1x) = -5x. Drop down the next term from the dividend to create -5x - 8.
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Divide the first term of the new expression, -5x, by the first term of the divisor, x: -5x / x = -5. Write the -5 (including the negative sign as a minus sign) in the second answer spot above the bracket. Multiply the -5 to the second term of the divisor: -5 * 1 = -5. Write the new expression, -5x + -5, under the other expression and subtract: (-5x - 8) - (-5x + -5) becomes (-5x - 8) + 5x + 5 = -3. Note that because there is no "x" left, the -3 is the remainder.
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Write the answer from the spot above the bracket: x - 5. Incorporate the remainder by adding a fraction with the remainder in the numerator and the divisor in the denominator. Write the final answer as x - 5 + (-3 / x + 1).
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