Exploring Synthetic Division Techniques

The video tutorial revisits synthetic division, focusing on handling remainders and writing solutions. It includes three examples: dividing polynomials by x+2, x+4, and x-1, with emphasis on managing missing degrees by inserting zeros. The tutorial explains each step in detail, ensuring a clear understanding of the process and how to express remainders over divisors.

What is the first step in synthetic division?

• Divide the coefficients

• Add the coefficients

• Set the divisor equal to zero

• Multiply the coefficients

In the first example, what is the divisor after setting x + 2 equal to zero?

• 2

• -2

• 1

• -1

What is the remainder in the first example problem?

• 5

• 7

• 12

• 6

How do you write the remainder in synthetic division?

• As a percentage

• As a decimal

• As a fraction over the divisor

• As a whole number

In the second example, what is the result of x cubed plus x squared minus 10x plus 13 divided by x plus 4?

• x squared - 3x + 2 + 6/(x+4)

• x squared - 3x + 2 + 5/(x+4)

• x squared - 3x + 2 + 1/(x+4)

• x squared - 3x + 2 + 7/(x+4)

What should you do if there is a missing degree in the polynomial?

• Insert a zero for the missing degree

• Subtract one from the degree

• Ignore it

• Add one to the degree

In the third example, what is the missing degree that needs a zero placeholder?

• x^3

• x^2

• x

• x^0

What is the remainder in the third example problem?

• 3

• 1

• 7

• 5

What is the final result of 3x^4 - 11x^3 + 13x^2 - 4 divided by x - 1?

• 3x^3 - 8x^2 + 5x + 5 + 1/(x-1)

• 3x^3 - 8x^2 + 5x + 5 + 2/(x-1)

• 3x^3 - 8x^2 + 5x + 5 + 6/(x-1)

• 3x^3 - 8x^2 + 5x + 5 + 7/(x-1)

Why is it important to include a zero for missing degrees in synthetic division?

• To simplify the coefficients

• To avoid confusion

• To ensure all degrees are accounted for

• To make the problem easier