Dividing Polynomials with Remainders

The video tutorial explains how to perform algebraic long division with polynomials. It begins by setting up the division problem, then walks through the division process step-by-step, including handling remainders. Finally, it verifies the results by multiplying the quotient and divisor to check if the original polynomial is obtained.

What was the initial mistake in the problem setup?

• The dividend was incorrect.

• The divisor was incorrect.

• The terms were not aligned properly.

• The coefficients were wrong.

How should the division problem be rewritten for algebraic long division?

• As a simple fraction.

• As a polynomial equation.

• With aligned terms for each power.

• With only the highest degree terms.

What is the first step in the division process?

• Divide the highest degree term of the dividend by the highest degree term of the divisor.

• Subtract the lowest degree term of the divisor from the dividend.

• Multiply the entire divisor by the highest degree term of the dividend.

• Add the highest degree terms of the dividend and divisor.

What do you do after multiplying the divisor by the first term of the quotient?

• Divide the result by the next term of the dividend.

• Add the result to the dividend.

• Subtract the result from the dividend.

• Multiply the result by the next term of the divisor.

What is the next step after aligning the terms and subtracting?

• Add the remainder to the quotient.

• Divide the remainder by the divisor.

• Bring down the next term of the dividend.

• Multiply the quotient by the divisor again.

When do you stop the division process?

• When the remainder is zero.

• When the degree of the remainder is less than the degree of the divisor.

• When the quotient is a constant.

• When the dividend is fully divided.

How is the final answer expressed?

• As the quotient plus the remainder divided by the divisor.

• As the quotient minus the remainder.

• As the quotient plus the remainder.

• As the quotient minus the remainder divided by the divisor.

What is the purpose of verifying the result?

• To simplify the quotient.

• To confirm the original dividend is obtained.

• To ensure the remainder is zero.

• To check if the quotient is correct.

What should you get when you multiply the quotient and the divisor?

• The original divisor.

• The original dividend.

• The remainder.

• A simplified polynomial.

What happens to the terms that cancel out during verification?

• They are subtracted from the quotient.

• They are added to the remainder.

• They are ignored.

• They confirm the correctness of the division.