Factoring a Five-Term Polynomial by Grouping

The video tutorial explains how to factor a five-term polynomial by grouping. Initially, the instructor attempts to group the first three and last two terms but finds it not factorable. A second attempt involves regrouping the first two and last three terms, leading to a successful factorization. The instructor further explores additional techniques, including factoring by grouping and using the difference of cubes, to finalize the solution.

What is the first step in factoring a five-term polynomial by grouping?

• Group the first three terms and the last two terms

• Use the quadratic formula

• Group all terms together

• Factor out the greatest common factor

Why was the initial quadratic trinomial not factorable?

• It was already in its simplest form

• It had no common factors

• The terms were not arranged correctly

• There was no combination of factors that worked

What method was used to factor the quadratic trinomial after re-grouping?

• The quadratic formula

• Synthetic division

• Completing the square

• The T method

What is the purpose of the T method in factoring?

• To find the greatest common factor

• To simplify the polynomial

• To solve the polynomial equation

• To determine the correct combination of factors

What common factor was identified in the re-grouped terms?

• x^2 + x + 1

• 2x - 3

• x - 4

• x - 1

How was the expression further factored after identifying the common factor?

• By using the quadratic formula

• By recognizing a difference of cubes

• By completing the square

• By using synthetic division

What is the significance of finding a zero in the polynomial?

• It indicates the polynomial is not factorable

• It shows the polynomial is already simplified

• It means the polynomial has no real roots

• It helps in identifying a factor of the polynomial

What is the result of factoring the expression x^3 + 2x - 3?

• x - 1

• 2x - 3

• x^2 + x + 1

• x - 4

What is the final factored form of the polynomial?

• (x - 4)(x - 1)(2x - 3)

• (x - 1)(x^2 + x + 1)(2x - 3)

• (x - 4)(2x - 3)(x + 1)

• (x - 4)(x - 1)(x^2 + x + 1)

What is the role of the difference of cubes in the factorization process?

• It indicates the polynomial is not factorable

• It provides a method to factor the expression

• It helps in simplifying the polynomial

• It shows the polynomial has complex roots