Adding and Subtracting Rational Expressions

The video tutorial covers the process of dividing polynomials using long division. It begins with a review of long division with basic numbers, then transitions to polynomial long division. The tutorial provides step-by-step examples, including handling missing powers and dealing with remainders. The instructor emphasizes the importance of placeholders for missing terms to avoid errors.

What is the result of dividing 101952 by 59?

• 1528

• 1628

• 1828

• 1728

What is the remainder when 5467 is divided by 13?

• 6

• 4

• 7

• 5

In polynomial long division, what is the quotient when dividing x^3 + 4x^2 - 16x + 8 by x - 2?

• x^2 + 6x - 4

• x^2 + 6x + 4

• x^2 - 6x + 4

• x^2 - 6x - 4

What is the remainder when dividing x^3 + 4x^2 - 16x + 8 by x - 2?

• 1

• 3

• 0

• 2

What is the correct approach to subtract terms in polynomial long division?

• Multiply like terms

• Subtract like terms only

• Subtract all terms

• Add like terms

How do you adjust the divisor in polynomial long division to match the highest degree of the dividend?

• Multiply to match the highest power

• Divide to match the highest power

• Add to match the highest power

• Subtract to match the highest power

What is the final quotient when dividing 2x^3 + 5x^2 - 19x + 12 by 2x + 7?

• x^2 + x - 6

• x^2 - x + 6

• x^2 + x + 6

• x^2 - x - 6

What is the quotient when dividing 3x^3 + 2x^2 - 37x + 12 by x + 4?

• 3x^2 + 10x + 3

• 3x^2 - 10x - 3

• 3x^2 + 10x - 3

• 3x^2 - 10x + 3

How do you handle missing powers in polynomial long division?

• Use zero placeholders

• Ignore the missing powers

• Guess the coefficients

• Stop the division

What is the remainder when dividing x^4 - 5x^2 + 1 by x^2 - x - 5?

• 2x - 6

• 2x - 5

• 2x + 5

• 2x + 6