Factoring Trinomials Using the AC Method

The video tutorial explains how to factor a trinomial using the AC method. It begins by identifying the coefficients 'a' and 'c', multiplying them, and finding two numbers that multiply to the product and add to the middle term. The process involves trial and error to find suitable factors. Once identified, the expression is rewritten, and factor by grouping is used to simplify it. The tutorial concludes with the final solution, emphasizing the importance of patience and different problem-solving approaches.

What is the first step in the AC method?

• Multiply the coefficients of the first and last terms.

• Add the coefficients of the trinomial.

• Subtract the last term from the first term.

• Divide the middle term by the first term.

Which two numbers multiply to 60 and add to -16?

• 1 and 60

• 3 and 20

• 4 and 15

• 6 and 10

Why do both numbers need to be negative in this problem?

• Because they need to multiply to a positive number.

• Because they need to multiply to a negative number.

• Because they need to add to a negative number.

• Because they need to add to a positive number.

How is the trinomial rewritten after finding the two numbers?

• By dividing the middle term by the two numbers.

• By multiplying the two numbers with the first term.

• By replacing the middle term with the two numbers.

• By adding the two numbers to the middle term.

What is the next step after rewriting the trinomial?

• Combine like terms.

• Multiply the terms.

• Factor by grouping.

• Simplify the expression.

What is the greatest common factor (GCF) of the first two terms in the rewritten trinomial?

• 2x

• 6

• 12x

• 6x

What do you multiply by 6x to get 12x squared?

• 12

• 2

• x

• 2x

What do you multiply by -5 to get -10x?

• 10x

• 5x

• x

• 2x

What is the final factored form of the trinomial?

• (2x + 1)(6x - 5)

• (2x + 1)(6x + 5)

• (2x - 1)(6x + 5)

• (2x - 1)(6x - 5)

Why is it important to check your work after factoring?

• To ensure the factors are correct.

• To rewrite the trinomial.

• To find the greatest common factor.

• To simplify the expression.