1.

First divide the first term in the divisor into the first term in the dividend.

When we subtract, we change the sign and add. Some people will put the changed sign over the original sign. That way, they can tell which one was the original sign and which one is the changed sign.

Multiply this term by the divisor and subtract it from the dividend. Divide the first term in the divisor into the first term in the remainder.

Repeat the process with the remainder.

This time the remainder has smaller degree than the divisor. We repeat the process until the remainder has smaller degree than the divisor which happens at this point. In this class, one can either leave their answer as a quotient and a remainder

x2 - 9x + 43   R   -212

or it is also customary to put the remainder over the divisor into a fraction.

or

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