Factoring Trinomials When a is Not Equal to 1

The video tutorial covers lesson 7.4 on factoring trinomials when 'a' is not equal to one. It begins with introductory exercises on factoring trinomials and proceeds to explain the steps involved in factoring when 'a' is not one. The lesson includes identifying the greatest common factor, using diamonds to rename the middle term, and solving by grouping. Two example problems are solved step-by-step, demonstrating the process of factoring and checking the solutions. The tutorial concludes with a final example and encourages students to practice further.

What is the factored form of x^2 - 10x + 24?

• (x - 8)(x - 3)

• (x - 12)(x + 2)

• (x - 6)(x - 4)

• x(x - 14) + 24

What is the result of factoring x^2 + 10x + 9?

• (x + 5)(x + 5)

• (x + 1)(x + 9)

• (x + 2)(x + 4)

• (x + 3)(x + 7)

What changes in the signs of the factors when the middle term's sign changes?

• No change in signs

• One sign becomes positive and one negative

• Both signs become negative

• Both signs become positive

What is the first step in factoring a trinomial when a is not equal to one?

• Set up a diamond

• Solve by grouping

• Look for a greatest common factor

• Identify the a, b, and c terms

What does the top number in a diamond represent in the context of factoring trinomials?

• The sum of a and c

• The product of a and c

• The difference between a and c

• The quotient of a and c

How do you check if your factoring of a trinomial is correct?

• By graphing the equation

• By foiling the factors

• By substituting values for x

• By setting the equation to zero

What is the factored form of 2x^2 + 13x + 6?

• (x + 12)(x + 1)

• (2x + 3)(x + 2)

• (2x + 1)(x + 3)

• (2x + 1)(x + 6)

What is the purpose of renaming the middle term in the diamond method?

• To determine the value of x

• To identify the greatest common factor

• To prepare for solving by grouping

• To simplify the equation

What is the factored form of 2x^2 - 9x + 9?

• (x - 6)(x - 3)

• (2x - 9)(x + 1)

• (2x - 3)(x + 3)

• (2x - 3)(x - 3)

What is the factored form of 6x^2 + 20x + 16?

• (6x + 8)(x + 2)

• (3x + 4)(2x + 4)

• (6x + 4)(x + 4)

• (2x + 4)(3x + 4)