Synthetic Division

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In this section, we learn how to divide a polynomial by a binomial of the form (x - k) using a process known as synthetic division. If we encounter a divisor of the form (x + k), we will re-write this divisor as: (x - (-k)). Up to this point, we have only seen polynomial division using long division with all information involved (both variables and numerical). Synthetic division is generally faster and used as a shortcut for this specific scenario, due to the fact that it uses the numerical information only. This is similar to when we used a matrix to solve a system of linear equations. We can save time by just working with the numerical information. This process is usually not used when we first learn how to divide polynomials, but comes into play when we are trying to find zeros (roots) of polynomials.
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