Factoring Patterns in Polynomials

The video tutorial explains how to factor expressions using patterns such as perfect squares and difference of squares. It provides examples to illustrate these patterns and guides viewers on identifying when a pattern is applicable or not. The tutorial encourages active participation by prompting viewers to pause and attempt factoring on their own.

What is the main goal when factoring expressions using patterns?

• To eliminate variables

• To increase the degree of the polynomial

• To identify a matching pattern

• To simplify the expression

What is the first step in identifying a pattern in a polynomial?

• Matching the polynomial to a known pattern

• Identifying perfect squares

• Simplifying the expression

• Checking for common factors

Which pattern is used to factor the expression u + v squared?

• u squared minus v squared

• u squared plus 2uv plus v squared

• u minus v squared

• u squared plus v squared

In the example of u + v squared, what is the value of u if u squared is 9x to the 8th?

• 9x to the 4th

• x to the 4th

• 3x to the 4th

• 3x to the 8th

Why was the perfect square pattern ruled out in the second example?

• The expression was already factored

• The middle term did not match 2uv

• The expression had more than three terms

• The terms were not perfect squares

What is the result of multiplying u plus v by u minus v?

• u squared plus v squared

• u squared minus v squared

• u squared plus 2uv plus v squared

• u squared minus 2uv plus v squared

In the difference of squares pattern, what is the value of v if v squared is y plus 3?

• 3

• y

• y plus 3

• y minus 3

What is a key characteristic of the difference of squares pattern?

• It involves adding and subtracting the same terms

• It results in a three-term polynomial

• It requires all terms to be positive

• It only applies to expressions with even exponents

Why couldn't the final example be factored using the difference of squares pattern?

• The terms were not perfect squares

• The expression had more than two terms

• The expression was already simplified

• The square root of one term was not an integer

Which of the following is not a pattern used in the video?

• Difference of squares

• Perfect square trinomial

• u minus v squared

• u plus v squared