Dividing Polynomials by Linear Expressions

The video tutorial explains how to divide polynomials, focusing on dividing a polynomial by x plus two. It begins with an introduction to the problem and the expected format of the answer. The instructor then provides a detailed, step-by-step walkthrough of the division process, emphasizing the importance of focusing on the highest degree terms first. The tutorial concludes with the final steps of the division, including handling the remainder and discussing domain conditions. The video encourages viewers to attempt the problem independently before following along with the solution.

What form should the answer take when dividing polynomials?

• A polynomial divided by another polynomial

• A polynomial with no remainder

• A clean polynomial or a polynomial plus a constant over x plus two

• A polynomial with a remainder

What is the first step in dividing x plus two into 3x^3 + 4x^2 - 3x + 7?

• Multiply the polynomial by x plus two

• Divide the highest degree term by x

• Subtract x plus two from the polynomial

• Divide the constant term by x plus two

How many times does x go into 3x^3?

• 3

• 3x^3

• 3x^2

• 3x

What do you do after multiplying 3x^2 by x plus two?

• Divide the result by x plus two

• Multiply the result by x

• Subtract the result from the original polynomial

• Add the result to the original polynomial

What is the next term in the quotient after 3x^2?

• -2x

• 2x

• -3x

• 3x

What is the result of subtracting -2x^2 times x plus two from the current polynomial?

• x^2 + 3x

• x + 4x

• x + 7

• x^2 - 3x

How many times does x go into x in the final step?

• 0 times

• 3 times

• 1 time

• 2 times

What is the remainder after completing the division?

• 7

• 1

• 2

• 5

How can the final answer be written?

• 3x^2 - 2x + 1 - 5/(x + 2)

• 3x^2 - 2x + 1 + 7/(x + 2)

• 3x^2 + 2x + 1 + 5/(x + 2)

• 3x^2 - 2x + 1 + 5/(x + 2)

What condition must be placed on the domain for the expressions to be identical?

• x cannot be equal to 0

• x cannot be equal to -2

• x cannot be equal to 1

• x cannot be equal to 2