Exploring Synthetic Division of Polynomials

This video tutorial focuses on dividing polynomial functions using synthetic division. It provides multiple examples, starting with dividing x cubed minus 2x squared minus five x plus six by x minus three, and continues with other examples, including cases with non-zero remainders and missing terms. The video concludes with a final example and a summary of the synthetic division process.

What is the first step in synthetic division when dividing a polynomial by x - 3?

• Write down the polynomial's coefficients.

• Add the coefficients together.

• Set x - 3 equal to zero and solve for x.

• Multiply the coefficients by 3.

In the first example, what is the quotient when x^3 - 2x^2 - 5x + 6 is divided by x - 3?

• x^2 + x - 2

• x^2 - x + 2

• x^2 + 2x - 1

• x^2 - 2x + 1

When dividing x^3 + 5x^2 + 7x + 2 by x + 2, what number is placed outside the synthetic division setup?

• 2

• 7

• 5

• -2

What is the quotient when x^3 + 5x^2 + 7x + 2 is divided by x + 2?

• x^2 + 2x + 1

• x^2 + 3x + 2

• x^2 + 3x + 1

• x^2 + 4x + 1

In the third example, what is the remainder when 3x^2 + 7x - 20 is divided by x + 5?

• 0

• 15

• 25

• 20

What is the quotient when 3x^2 + 7x - 20 is divided by x + 5?

• 3x + 7

• 3x - 7

• 3x + 8

• 3x - 8

Why is it important to include zero coefficients in synthetic division?

• To make the division process easier.

• To ensure the polynomial is in standard form.

• To avoid incorrect results.

• To simplify the polynomial.

What is the quotient when 7x^3 + 6x - 8 is divided by x - 4?

• 7x^2 + 30x + 120

• 7x^2 + 30x + 118

• 7x^2 + 28x + 120

• 7x^2 + 28x + 118

In the fifth example, what is the quotient when 3x^4 - 5x^2 + 6 is divided by x - 2?

• 3x^3 + 6x^2 + 7x + 14

• 3x^3 + 5x^2 + 7x + 12

• 3x^3 + 5x^2 + 7x + 14

• 3x^3 + 6x^2 + 7x + 12

What is the remainder when 3x^4 - 5x^2 + 6 is divided by x - 2?

• 36

• 34

• 32

• 28