Factoring Higher Degree Polynomials by Grouping

The video tutorial covers the process of factoring higher degree polynomials, focusing on techniques such as factoring by grouping. It explains how to factor cubic polynomials and apply these methods to solve practical problems, like finding dimensions of a rectangular prism. The tutorial also touches on advanced factoring techniques and provides a comprehensive guide to understanding and applying these methods effectively.

What is the main objective of this section?

• To factor higher degree polynomials by grouping

• To solve quadratic equations

• To learn about polynomial division

• To understand the properties of exponents

In the method reviewed from section 8-6, what is the first step in factoring trinomials?

• Group the terms

• Factor out the GCF

• Rewrite the middle term as the sum of two monomials

• Use the distributive property

When factoring the cubic polynomial 3n^3 - 12n^2 + 2n - 8, what is the common factor of the first two terms?

• 2n

• n^2

• 3n^2

• 3n

What must be true about the binomials left over after grouping for the technique to work?

• They must be different

• They must be prime

• They must be exactly the same

• They must have opposite signs

In the example 8p^3 + 14t^2 + 20t + 35, what is the common factor of the first two terms?

• 4t

• 5t

• 2t^2

• 2t

How is the method used in problem 1 similar to the method used in section 8-6?

• Both involve factoring out the GCF

• Both use the quadratic formula

• Both use the grouping technique

• Both require polynomial division

What is the first step in factoring the volume of the rectangular prism 6x^3 + 19x^2 + 15x?

• Group the terms

• Rewrite the middle term

• Factor out the GCF

• Use the quadratic formula

What are the possible dimensions of the rectangular prism with volume 6x^3 + 19x^2 + 15x?

• x, 2x + 5, 3x + 3

• x, 2x + 3, 3x + 5

• x, 3x + 5, 2x + 3

• x, 3x + 3, 2x + 5

What should you always do first when factoring polynomials?

• Rewrite the middle term

• Factor out the greatest common factor

• Group the terms

• Use the quadratic formula

If the polynomial has four or more terms, what technique should you use?

• Quadratic formula

• Polynomial division

• Grouping

• Completing the square