Dividing with algebra tiles involves visually representing a polynomial division problem to find the quotient. The quotient represents the width of the rectangle formed by the tiles.
Here's a breakdown of the process based on the provided reference:
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Set up the problem: Represent the dividend (the polynomial being divided) with the appropriate algebra tiles.
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Form a rectangle: Arrange the tiles into a rectangle, where one side of the rectangle represents the divisor (the polynomial you are dividing by).
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Determine the quotient: The remaining side of the rectangle represents the quotient.
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Example: As shown in the reference, when dividing x2 + 5x + 4 by x + 1, you arrange the tiles to form a rectangle with a width of x + 1. The length of that rectangle will be x + 4. Therefore (x2 + 5x + 4) / (x + 1) = x + 4. According to the reference, "So x squared plus 5x plus 4 divided by X plus one equals X plus four."
In essence, algebra tiles provide a visual and tactile way to understand polynomial division, by demonstrating how polynomials can be factored into rectangular areas. The divisor is one dimension of the rectangle, the dividend is the area, and the quotient is the other dimension.
