Learn how to simplify a trigonometric expression by factoring by grouping

The video tutorial covers various factoring techniques, including factoring by the greatest common factor (GCF), factoring trinomials, and special cases like the difference of squares and grouping. The instructor provides examples and explains how to apply these techniques to different polynomial expressions, emphasizing the importance of identifying the correct method based on the number of terms and their properties.

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

• Subtract the GCF from each term

• Divide each term by the GCF

• Add the GCF to each term

• Multiply all terms by the GCF

Which of the following is a characteristic of the difference of two squares?

• It is only applicable to linear terms

• It can be factored into a product of binomials

• It results in a sum of squares

• It involves three terms

When using the grouping technique, what is the first step?

• Factor out the GCF from the entire polynomial

• Group the first two terms and the last two terms

• Multiply all terms by a common factor

• Add a constant to each term

What is the GCF of the terms cosecant squared of X and cosecant of X?

• Cosecant squared of X

• Cosecant of X

• Cosecant cubed of X

• 1

How can you verify your answer when factoring by GCF?

• By using the distributive property

• By adding all terms together

• By multiplying the terms by zero

• By subtracting the GCF from each term

In the grouping technique, why is it important to have the same binomial in both groups?

• To make the polynomial quadratic

• To allow for further factoring

• To simplify the expression into a single term

• To ensure the polynomial is linear

What should you do if the terms in the grouping technique have different signs?

• Add a constant to each term

• Multiply all terms by a common factor

• Factor out a negative one from one of the groups

• Ignore the signs and proceed