Polynomial Long Division Concepts

Nancy explains how to use long division to divide polynomials, starting with a simple example and progressing to a more complex one with missing terms. She highlights the importance of placeholders and careful subtraction to avoid common mistakes. The video concludes with tips to prevent errors and a reminder to like the video.

What is the first step in setting up a polynomial long division problem?

• Add a placeholder for missing terms.

• Multiply the polynomials first.

• Re-write the expression in the division form used in elementary school.

• Divide the coefficients directly.

When performing long division, where do you place the first term of the quotient?

• In line with the constant term.

• In line with the corresponding term in the dividend.

• Above the highest degree term of the divisor.

• Above the highest degree term of the dividend.

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

• Add the result to the dividend.

• Subtract the result from the dividend.

• Multiply the result by the next term.

• Divide the result by the next term.

How do you handle the remainder in polynomial long division?

• Ignore it.

• Multiply it by the divisor.

• Place it over the divisor.

• Add it to the quotient.

What is crucial to remember when a term is missing in the polynomial?

• Multiply the missing term by one.

• Add a zero placeholder for the missing term.

• Divide the missing term by the divisor.

• Skip the missing term.

In a complex polynomial division, what is the first step after rewriting the expression?

• Find the highest power of x in the divisor.

• Multiply the entire expression by zero.

• Subtract the divisor from the dividend.

• Determine how many times the divisor's leading term fits into the dividend's leading term.

What should you do if you encounter a sign error during subtraction?

• Add a positive sign instead.

• Multiply the entire expression by negative one.

• Correct it by ensuring the negative sign is distributed properly.

• Ignore it and continue.

Why is it important to use parentheses during subtraction in polynomial division?

• To add complexity to the problem.

• To separate the terms visually.

• To ensure the negative sign is applied to all terms.

• To make the expression look neat.

What is the final step in polynomial long division?

• Subtract the remainder from the quotient.

• Write the remainder over the divisor.

• Add the remainder to the quotient.

• Multiply the remainder by the divisor.

What common mistake should be avoided in polynomial long division?

• Dividing instead of multiplying.

• Adding instead of subtracting.

• Not writing the zero placeholder for missing terms.

• Forgetting to multiply the terms.