Factoring and GCF Problems

This video tutorial explains how to factor trinomials with at least two variables. It begins by introducing the concept and then demonstrates the process of finding two numbers that multiply to a specific value and add to another. The tutorial covers factoring by grouping, verifying the solution, and provides examples for practice. The video concludes with a second example and encourages viewers to practice the techniques discussed.

What is the first step in factoring a trinomial with two variables?

• Add the coefficients of the terms

• Multiply the leading coefficient by the last coefficient

• Subtract the last coefficient from the leading coefficient

• Divide the middle coefficient by the leading coefficient

Which pair of numbers multiplies to -6 and adds to 5?

• 2 and 3

• -2 and 3

• 1 and -6

• -1 and 6

What is the greatest common factor (GCF) of the terms 3a^2 and 6ab?

• 6b

• 3a

• 3b

• 6a

When factoring by grouping, what should you do if the terms have a negative sign?

• Add the negative sign to the GCF

• Ignore the negative sign

• Factor out the negative sign

• Multiply the terms by -1

How can you verify if the factored expression is correct?

• By multiplying the expression by 2

• By dividing the expression by the GCF

• By using the FOIL method

• By adding the coefficients

What is the result of multiplying 6 by -4 in the second example?

• -24

• 24

• -20

• 20

Which pair of numbers multiplies to -24 and adds to 5 in the second example?

• -3 and 8

• 2 and 12

• 3 and 8

• -2 and 12

What is the GCF of the terms 6x^2 and 3xy?

• 3x

• 6y

• 6x

• 3y

In the second example, what is the GCF of the terms 8xy and 4y^2?

• 8y

• 4x

• 4y

• 8x

What is the final factored form of the expression in the second example?

• (2x - 4y)(3x + y)

• (3x + 4y)(2x - y)

• (2x + 4y)(3x - y)

• (3x - 4y)(2x + y)