Identify the algebraic term in the numerator, which is the top of the fraction, and the denominator, which is the bottom of the fraction. For example, when dividing 3x^2 ' 11x ' 4 divided by x - 4, identify x - 4 as the denominator and 3x^2 ' 11x ' 4 as the numerator.
Write the denominator expression as the divisor in a division equation and the numerator as the dividend. In the case of 3x^2 ' 11x ' 4 divided by x - 4, x - 4 will be the divisor on the left side of the division equation, and 3x^2 ' 11x ' 4 is the dividend inside the division equation.
Solve as a normal division equation, but with variables replacing numbers. When dividing 3x^2 ' 11x ' 4 by x - 4, start by looking at how many times 1x will fit in 3x^2.
Multiply the dividend by the first variable of a quotient when you discover it and write the answer under the dividend. Subtract the two expressions. Bring down the next part of the dividend expression to the second row. In the example, 3x is the beginning of the dividend, and the second row is 3x^2 - 12x. Bringing down the next part of the dividend results in x - 4.
Determine how much of the divisor can be divided into the second row under the dividend. Write the second part of the quotient on top of the dividend and multiply it by the divisor. In the case of 3x^2 ' 11x ' 4 divided by x - 4, the second part of the quotient will be plus 1.
Subtract the third row from the second row. If the dividend expression is only three variables long and the subtraction equals zero, then you are done. If it does not equal zero, then you have a remainder that can be written as a fraction with the divisor as the denominator and the remainder as the numerator. If the expression is more than three variables, continuing dividing until you reach the end of the expression. In the case of 3x^2 ' 11x ' 4 divided by x - 4, 3x + 1 is the final result and no further calculation is needed.
Check your answer by multiplying the divisor by the quotient. If it equals the dividend, you successfully solved an algebraic division equation. If not, recheck your work for mistakes. In the case of 3x^2 ' 11x ' 4 divided by x - 4, 3x + 1 times x - 4 equals 3x^2 ' 11x ' 4.