Factoring Trinomials: A Comprehensive Guide

The video tutorial explores an alternative technique for factoring trinomials with a leading coefficient other than one. It introduces the method of grouping, which involves keeping the first and last terms and splitting the middle term into two, resulting in four terms. The video provides multiple examples, demonstrating how to apply the grouping method, identify common factors, and ensure the binomials match. The tutorial emphasizes the importance of checking the middle term and adjusting signs based on the last term's sign.

What is the first step in factoring trinomials with a leading coefficient other than one?

• Apply the quadratic formula

• Split the middle term immediately

• Look for a GCF

• Check if it's a perfect square trinomial

What method is introduced for factoring trinomials in the video?

• Trial and error

• Synthetic division

• Grouping method

• Quadratic formula

How do you determine how to split the middle term in the grouping method?

• Divide the middle term by 2

• Add the leading coefficient and the constant term

• Use the quadratic formula

• Multiply the leading coefficient by the constant term

What is the result of multiplying the leading coefficient and the constant term in the first example?

• 12

• 6

• 8

• 10

In the example with positive signs, what factors of 6 add up to 7?

• 2 and 5

• 1 and 6

• 3 and 4

• 2 and 4

How many terms does the problem have after splitting the middle term?

• Five

• Two

• Three

• Four

What sign rules are applied when the last term is positive?

• Both terms will have different signs

• Both terms will have positive signs

• Both terms will have negative signs

• Signs of the terms do not matter

What do you hope to achieve by grouping in the factoring process?

• No common factors

• A common monomial

• A common binomial

• A common trinomial

In the example with negative signs, what are the factors that subtract to give the middle term?

• -3 and -2

• -6 and 1

• 3 and -2

• 6 and -1

What is the GCF in the final example provided?

• x - 1

• x + 2

• 2x + 5

• 3x + 1