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Section 4.2: Synthetic Division
Synthetic division is a shorthand, or shortcut, method of polynomial division in the special case of dividing by a linear factor -- and it only works in this case. Synthetic division is generally used, however, not because it's part of a curriculum, but because it's so much quicker and easier than the alternatives.
To set up the division, you write the coefficients of the polynomial you're dividing in a row. If there is a missing term (for example, if there is no x² term), you must include a 0 as a placeholder.
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