- 1). 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.
- 2). 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.
- 3). 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.
- 4). 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).
previous post
next post