Mastering Polynomial Long Division Techniques

The video tutorial provides a comprehensive guide on performing long division with polynomials. It begins with an introduction to the concept, followed by a basic arithmetic example to illustrate the process. The tutorial then explains how to set up polynomial division problems, emphasizing the importance of arranging terms in descending order and using zero terms for missing degrees. Through detailed examples, the video demonstrates the step-by-step process of dividing polynomials, including handling remainders. The tutorial concludes with additional examples and a summary of key points.

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

• Subtract the terms

• Identify the remainder

• Multiply the terms

• Set up the dividend and divisor

When performing long division with polynomials, what do you do if a term is missing?

• Add the missing term to the divisor

• Use a placeholder term with a coefficient of 0

• Use a placeholder term with a coefficient of 1

• Ignore the missing term

In the example problem, what is the first term in the quotient when dividing x^3 by x?

• x^3

• x

• x^2

• 1

What operation is performed after multiplying the terms in long division with polynomials?

• Addition

• Division

• Multiplication

• Subtraction

In the second example, what is the result of dividing -12x by x?

• -12

• 12

• -x

• x

How do you handle subtraction when performing long division with polynomials?

• Add the opposite

• Ignore the subtraction

• Subtract directly

• Multiply by -1

In the third example, what is the quotient when dividing y^3 + 27 by y + 3?

• y^2 - 9

• y^2 + 3

• y^2 - 3

• y^2 + 9

What is the remainder when dividing y^3 + 27 by y + 3?

• 0

• 3

• 27

• 9

In the final example, what is the first term in the quotient when dividing 24x^3 by 8x?

• 8x

• 8x^2

• 3x

• 3x^2

What is the final quotient when dividing the polynomial in the last example?

• 3x^2 + 5x + 7 - 4/(8x + 3)

• 3x^2 - 5x - 7 + 4/(8x + 3)

• 3x^2 + 5x + 7 + 4/(8x + 3)

• 3x^2 - 5x - 7 - 4/(8x + 3)