Exploring Factoring Techniques for Polynomials

In this video, the teacher explains how to factor trinomials and polynomials. The video begins with an introduction to trinomials, focusing on the 'easy style' where the coefficient of the squared term is one. The teacher demonstrates the cross method for factoring these trinomials. The video then progresses to more complex trinomials where the coefficient is greater than one, using the cross method and identifying the greatest common factor (GCF). Finally, the video covers factoring four-term polynomials by grouping terms and finding the GCF. Throughout, the teacher provides examples and encourages viewers to practice.

What is the definition of a trinomial?

• A polynomial with two terms

• A polynomial with three terms

• A polynomial with four terms

• A polynomial with one term

What makes a trinomial an 'easy style' for factoring?

• When the coefficient of the squared term is 1

• When there is no constant term

• When the coefficient of the squared term is greater than 1

• When the coefficient of the squared term is 0

What is the purpose of the cross method in factoring?

• To solve quadratic equations

• To identify the factors of a trinomial

• To divide polynomials

• To find the greatest common factor

What do the two numbers found using the cross method need to do?

• Add up to the coefficient of the linear term

• Multiply to give the constant and add to give the coefficient of the linear term

• Divide the squared term evenly

• Multiply to the coefficient of the squared term

How do you factor a trinomial when the coefficient of the squared term is greater than 1?

• By dividing each term by the coefficient of the squared term

• By using the cross method with adjustments

• By finding the square root of the constant term

• By using the quadratic formula

In the context of factoring, what does 'splitting the middle' refer to?

• Separating the constant term from the polynomial

• Breaking down the middle term into two terms that can be factored

• Using the GCF to divide the polynomial

• Dividing the polynomial into two equal parts

What is the first step in factoring four-term polynomials?

• Finding the least common multiple

• Applying the quadratic formula

• Grouping the first two and the last two terms

• Multiplying all terms together

What is the role of the Greatest Common Factor (GCF) in factoring polynomials?

• It is added to each term in the polynomial

• It is divided out of the terms in a group to simplify

• It is subtracted from each term in the polynomial

• It is used to multiply the remaining terms

What is the result of factoring a four-term polynomial by grouping?

• A single polynomial expression

• A binomial and a trinomial

• Two binomials

• Two trinomials

How do you determine the GCF in a group of terms?

• By identifying the term with the lowest coefficient

• By adding all the coefficients together

• By identifying the common factor that can divide each term in the group

• By finding the highest exponent in the group