Factor by Grouping Techniques

The video tutorial explains how to factor polynomials using the grouping method. It begins with an introduction to different factoring techniques, including binomials, trinomials, and the greatest common factor. The main focus is on the grouping method, which is used for polynomials with an even number of terms, typically four. The tutorial provides three examples of factoring by grouping, demonstrating how to identify and factor out the greatest common factor from grouped terms. It concludes with solving polynomial equations by setting them equal to zero and applying the zero product rule.

What is the first step in factoring a polynomial using the grouping method?

• Identify the greatest common factor (GCF) of all terms.

• Expand the polynomial.

• Combine like terms.

• Group the polynomial into pairs of terms.

When using the grouping method, what should you do after grouping the terms?

• Subtract the terms.

• Identify the GCF for each group.

• Multiply the terms.

• Add the terms together.

In the example given, what is the GCF of the first group (x^3 - 5x^2)?

• x^2

• x

• x^3

• 5

What is the goal of factoring by grouping?

• To simplify the polynomial.

• To identify a common factor in each group.

• To expand the polynomial.

• To find the sum of the terms.

What should you do if the polynomial does not have a common factor after grouping?

• Combine like terms.

• Expand the polynomial.

• Factor by grouping will not work.

• Continue with the next step.

What is the common factor in the example involving x^3 and 9x^2?

• x

• x^3

• 9

• x^2

What must be true for a polynomial equation before solving by factoring?

• The polynomial must be expanded.

• The polynomial must be equal to zero.

• The polynomial must have no common factors.

• The polynomial must be simplified.

What is the zero product rule used for?

• To expand the polynomial.

• To combine like terms.

• To identify the GCF.

• To find the roots of the polynomial.

What should you do if you encounter a negative value under the square root while solving?

• Take the absolute value.

• Square the negative value.

• Ignore the negative value.

• Use the imaginary unit 'i'.

How many solutions are there for a polynomial with the highest exponent of 3?

• 4

• 3

• 2

• 1