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Long division is useful with the remainder and factor theorems, but long
division can be time consuming. To divide a polynomial by a binomial and
compute the remainder, we can also use synthetic division. We can only
divide by a binomial whose leading
coefficient is 1--thus, we must factor the
leading coefficient out of the binomial and divide by the leading coefficient
separately. Also, the binomial must have degree 1; we cannot use synthetic
division to divide by a binomial like x2 + 1. Here are the steps for
dividing a polynomial by a binomial using synthetic division:
Example: What is the result when 4x4 -6x3 -12x2 - 10x + 2 is
divided by x - 3? What is the remainder?
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