Factoring Techniques and Patterns

The video tutorial by Mr. Witt from Fort Benton Tutoring covers the topic of factoring with radicals. It provides a detailed walkthrough of ten different problems, each demonstrating various factoring techniques such as finding the greatest common factor (GCF), using the difference of squares, and applying the perfect square trinomial pattern. The tutorial emphasizes the importance of recognizing patterns and provides tips for simplifying expressions. Mr. Witt also highlights the use of exponential notation and the AC method for factoring quadratic trinomials.

What is the first step in the general strategy for factoring expressions?

• Look for the greatest common factor (GCF)

• Identify the difference of squares

• Apply the AC method

• Use substitution

In Problem 1, what common factor is identified in the expression?

• Square root of 3

• Square root of 5

• Square root of 2

• Square root of 7

What is the GCF in Problem 2?

• Square root of 3

• 15

• 5

• Square root of 6

Which pattern is used to factor quadratic binomials?

• Factoring by grouping

• AC method

• Difference of squares

• Sum of cubes

In Problem 3, what is the result of applying the difference of squares pattern?

• (x + √5)(x - √5)

• (x + √7)(x - √7)

• (x + √3)(x - √3)

• (x + √2)(x - √2)

What is the focus when factoring quadratic trinomials with radicals in Problem 4?

• Recognizing common radical factors

• Identifying perfect squares

• Finding factors of the middle term

• Using the AC method

In Problem 5, what is the first step in applying the difference of squares pattern?

• Open parentheses

• Use substitution

• Identify the GCF

• Find the square root of each term

What is recognized in Problem 6 to simplify the expression?

• A perfect square trinomial

• A difference of cubes

• A sum of squares

• A common factor

How is the expression rewritten in Problem 7 to facilitate factoring?

• As a sum of cubes

• In exponential notation

• As a difference of squares

• Using substitution

In Problem 8, what is the key factor to focus on when factoring the trinomial?

• The constant term

• The middle term

• The square root of 5

• The coefficient of the first term