Factoring by Grouping Techniques

The video tutorial introduces the grouping method for factoring expressions, emphasizing the need for expressions with at least four terms. It explains the foiling and distributive property as foundational concepts. The tutorial provides a step-by-step guide to factoring by grouping, followed by examples to illustrate the method. Advanced techniques and considerations are also discussed, highlighting the flexibility and challenges of the grouping method.

What is the minimum number of terms required in an expression to use the grouping method?

• 4

• 5

• 2

• 3

Which method is commonly used to multiply binomials?

• Cross multiplication

• Distributive property

• FOIL method

• Long division

What should you always check for first when factoring any expression?

• The number of terms

• The leading coefficient

• The degree of the polynomial

• A common factor

When factoring by grouping, what must be true about the groups you create?

• They must all be positive

• They must have the same number of terms

• They must all be odd

• They must all be even

In the example where 18x^3 + 12x^2 + 21x + 14 is factored by grouping, what is the GCF of the first group (18x^3 and 12x^2)?

• 6x

• 3x^2

• 3x

• 6x^2

What should you do if the terms in a group are both negative when factoring by grouping?

• Factor out a negative GCF

• Ignore the negative sign

• Add a positive number

• Multiply by -1

What is the common factor in the expression 2n^3 - 1 and 4n^6 - 2n^3?

• 2n^3 - 1

• 4n^6

• 2n^3

• 1

What happens if the terms in the groups do not have a common factor when factoring by grouping?

• The expression is fully factored

• The expression is prime

• The expression is simplified

• The expression is multiplied

In the example 30h^5 + 15h^3 + 6h^2 + 4, what is the GCF of all the terms?

• 1

• h^2

• h

• 2

What should you do if the leading term of an expression is negative when factoring by grouping?

• Add a positive number

• Multiply by -1

• Ignore the negative sign

• Factor out a negative GCF