1.

We run through the steps for doing long division of polynomials. Divide the first term in the divisor into the first term in the dividend.

Multiply this term in the quotient by the divisor and subtract.

When we subtract, we need only bring down the next term from the dividend. Repeat this process with the remainder. Divide the first term in the divisor into the first term in the remainder.

Multiply this term in the quotient by the divisor and subtract.

Repeat this process with the remainder. Divide the first term in the divisor into the first term in the remainder.

Multiply this term in the quotient by the divisor and subtract.

At this point the remainder has smaller degree than the divisor, so we form a fraction by putting the remainder over the divisor and adding it to the quotient. The answer is

or

Check: Multiply the quotient times the divisor and add the remainder.

Note the correspondences between the multiplication and division problems.

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