The Visual / Auditory / Symbolic / Kinesthetic Approach to Algebra

 Algebraic Division

Algebraic division has the same algorithm, procedure, as regular division.

DIVISION
 1st: Use a blank rectangular sheet of paper to separate the storage region from the display area and to create a border for the rectangular area. 2nd: Represent the divisor vertically in storage on the left edge of the display area. 3rd: Represent the dividend in the display area in descending order beginning with the upper left corner. 4th: Arrange, if possible, the dividend in IDENTICAL rows in the display area. Matching one row per vertical divisor tile leaves remainders extra in the storage area. 5th: Once a single rectangular arrangement of tiles (extra remainder tiles excluded) is created, represent the appropriate quotient horizontally in the storage area as dictated by the dividend. 6th: If a single rectangular arrangement of tiles is not possible, add zeros as needed to fill the required area. 7th: Read the quotient and the remainder.

The work and answer for each of these problems is shown below and individually through the arrow.

 ex. 1. Divide 4x-12 by 4. ex. 5. Divide (x² - 4x + 3) / (x-1) ex. 2. Divide (x²+x) ÷ x ex. 6. Divide x² - x - 6 by x-3. ex. 3. Divide (2x³+6x²-2x+1) / (2x) ex. 7. Divide x² + 7x - 11 by x-5. ex. 4. Divide (x² + 4x + 3) / (x+3)

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