Factoring Trinomials Using the Bottoms Up Method

This video tutorial explains how to factor trinomials in the form of ax^2 + bx + c using the Bottoms Up method when 'a' is not equal to 1 and is not a common factor. The method involves rewriting the trinomial with 'a' equal to 1 by replacing c with a*c, factoring the new trinomial, and then adjusting the factors by dividing the constants and moving the denominators to the coefficients. Two example problems are provided to illustrate the process.

What is the primary focus of the Bottoms Up method in factoring trinomials?

• When 'C' is a prime number

• When 'A' is not equal to 1 and not a common factor

• When 'A' is a common factor

• When 'A' is equal to 1

How do you initially modify the trinomial in the Bottoms Up method?

• By dividing A by C

• By adding A to C

• By replacing C with A x C

• By subtracting B from A

What is the next step after rewriting the trinomial with 'A' equal to 1?

• Multiplying the trinomial by a constant

• Factoring the modified trinomial into two binomials

• Solving for the roots of the trinomial

• Finding the factors of the original trinomial

How do you adjust the factors of the modified trinomial?

• By dividing each constant term by the original 'A'

• By adding the original 'A' to each factor

• By multiplying each factor by the original 'A'

• By subtracting the original 'A' from each factor

What does the 'Bottoms Up' step involve?

• Adding the denominators to the constant terms

• Moving the denominators to the position of coefficients

• Switching the signs of the factors

• Moving the numerators to the position of coefficients

What is the purpose of verifying the product of the factors?

• To find the roots of the trinomial

• To confirm the correct factorization

• To ensure the trinomial is simplified

• To check if the trinomial is a perfect square

In the second example, what is the product of A and C?

• 20

• 80

• 60

• 40

What are the factors of 60 that add up to 19 in the second example?

• 20 and -1

• 10 and 9

• 15 and 4

• 12 and 5

How are the simplified denominators used in the second example?

• They are subtracted from the constant terms

• They are moved to the position of coefficients

• They are multiplied by the coefficients

• They are added to the constant terms

What are the final factors of the trinomial in the second example?

• X + 3 and X + 4

• 3X + 4 and 5X + 1

• 4X + 3 and 5X + 1

• 2X + 5 and 3X + 4