Factoring Polynomials and Techniques

This video tutorial focuses on factoring cubic polynomials. It begins with an introduction to factoring by grouping, demonstrating the method with examples. The video then explores cases where grouping is not applicable, introducing synthetic division as an alternative approach. The tutorial concludes with a summary of the methods discussed and encourages practice.

What is the first step in factoring the polynomial x^3 + 2x^2 - 5x - 10 by grouping?

• Apply the difference of squares technique

• Check if the ratios of coefficients allow grouping

• Use the quadratic formula

• Find the greatest common factor of all terms

In the polynomial 4x^3 - 8x^2 + 6x - 12, what is the greatest common factor of the first two terms?

• 6x

• 4x^2

• 8x^2

• 2x

After factoring x^3 + 3x^2 - 4x - 12 by grouping, what technique is used to further factor x^2 - 4?

• Difference of squares

• Completing the square

• Synthetic division

• Quadratic formula

Why can't the polynomial in the fourth section be factored by grouping?

• It is already in its simplest form

• The terms are not divisible by a common factor

• It is a quadratic polynomial

• The coefficients do not have the same ratio

What is the purpose of finding rational zeros in a polynomial?

• To simplify the polynomial

• To identify possible factors of the polynomial

• To determine the degree of the polynomial

• To convert the polynomial into a quadratic

Which number is found to be a solution for the polynomial using synthetic division in the fourth section?

• 1

• -1

• 2

• 3

What is the result of synthetic division when using x = 2 for the polynomial in the fourth section?

• x^2 - 5x + 6

• x^2 + 3x - 4

• x^2 - 2x - 3

• x^2 + 2x + 3

What are the factors of the trinomial x^2 - 2x - 3?

• (x + 2)(x - 3)

• (x - 2)(x + 3)

• (x + 3)(x - 1)

• (x - 3)(x + 1)

What is the final factorization of the polynomial after using synthetic division with x = -1?

• (x + 3)(x - 2)(x - 1)

• (x - 3)(x + 2)(x + 1)

• (x + 3)(x + 2)(x - 1)

• (x - 3)(x - 2)(x + 1)

What should you do if a polynomial cannot be factored by grouping?

• Apply the difference of squares

• Leave it unfactored

• Try synthetic division

• Use the quadratic formula