Exploring Polynomial Long Division and Synthetic Division

This video lesson covers polynomial long division and synthetic division. It begins with a review of long division using integers, emphasizing the importance of understanding this process before tackling polynomials. The instructor then demonstrates polynomial long division with examples, including cases with and without remainders. The lesson concludes with an introduction to synthetic division, showcasing its efficiency compared to traditional long division.

What is the first step in performing long division with integers?

• Add the divisor to the dividend

• Rewrite the division problem in long division format

• Subtract the divisor from the dividend

• Multiply the divisor by the dividend

When dividing 414 by 3, what is the first number you bring down after the initial subtraction?

• 4

• 11

• 14

• 1

In polynomial long division, what do you multiply the divisor by to get the first term of the dividend?

• The last term of the dividend

• The first term of the dividend

• The first term of the divisor

• The entire dividend

What is the result of dividing x^2 + 4x - 21 by x + 7?

• x + 3

• x - 3

• x + 7

• x - 7

When dividing 2x^2 + 5x + 15 by x - 3, what is the remainder?

• 33

• 11

• 48

• 15

How do you write the final answer when there is a remainder in polynomial long division?

• As a whole number

• As a fraction with the remainder over the divisor

• As a mixed number

• As a decimal

What placeholder term is added when a polynomial is missing a term during long division?

• 0

• 0x^3

• 0x

• 0x^2

In synthetic division, what number do you use to divide when the divisor is x - 1?

• 1

• 3

• 0

• 2

What is the first step in synthetic division after setting up the coefficients?

• Subtract the coefficients

• Multiply the coefficients

• Add the coefficients

• Drop down the first coefficient

What is the final step in synthetic division?

• Multiply the last two numbers

• Add the last two numbers

• Write the remainder over the original divisor

• Subtract the last two numbers