Long division of polynomials is done with the same basic algorithm that is used for long division of integers. Here, you look at the first term of the binomial (divisor) and decide what it needs to be multiplied by in order to get the first term of the polynomial (dividend). Write that monomial on top of the division bar, multiply it by both terms of the binomial, and write your answer below the polynomial. Subtract vertically, and the first term should be eliminated. Repeat this process: look again at the first term of the binomial and decide what it needs to be multiplied by in order to get the first term of the difference. Repeat this over and over. Your quotient is whatever is on the top of the division bar, and the remainder is the bottom right value that your dividend cannot multiply in to.
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