Factoring Quadratic Trinomials with Diamond Grouping

This video tutorial from mathgotserved.com teaches students how to factor quadratic trinomials using the diamond grouping or X game method. It includes two detailed examples: one with positive terms and another with a negative linear term. The tutorial emphasizes the importance of checking work through expansion and provides practice problems for mastery. The video concludes with a summary and encourages viewers to engage with additional resources on the website.

What method is primarily discussed in the tutorial for factoring quadratic trinomials?

• Square completion

• X game method

• Quadratic formula

• Graphical analysis

What is the first step in the X game method of factoring?

• List all factor pairs of AC

• Divide the middle term into two parts

• Draw a diamond shape

• Identify the a, b, and c values

In the example of 15x^2 + 16x + 4, what are the values of a, b, and c?

• a=16, b=15, c=4

• a=15, b=4, c=16

• a=15, b=16, c=4

• a=4, b=16, c=15

What does the AC value represent in the X game method?

• Product of a and c

• Sum of a and c

• Difference between a and c

• Quotient of a and c

How do you verify the correctness of the factored form of a quadratic trinomial?

• By differentiation

• By integration

• By graphing

• By expansion

What is the factored form of 15x^2 + 16x + 4?

• (5x + 4)(3x + 2)

• (5x + 2)(3x + 2)

• (3x + 2)(5x + 2)

• (3x + 2)(5x + 4)

What special consideration is needed when the middle term of the quadratic trinomial is negative?

• Use only positive integers in the X game

• Multiply a and c by -1 before proceeding

• Factor out a negative from one of the groups

• Ignore the negative sign during the AC method

What is the factored form of 7x^2 - 15x + 2?

• (x - 2)(7x + 1)

• (x - 2)(7x - 1)

• (7x - 1)(x - 2)

• (7x + 1)(x - 2)

How does the sign of the middle term affect the signs of the numbers found in the X game?

• The sign of the numbers does not matter

• Both numbers are positive

• Both numbers are negative

• One number is positive, the other is negative

What should you do after factoring a quadratic trinomial to ensure it is correct?

• Check with a calculator

• Ask a peer to review

• Expand and compare to the original

• Substitute values to check