Factoring Quadratic Trinomials by Grouping

This video is the third part of a series on factoring quadratic trinomials by grouping. It begins with an introduction to the method and a review of previous parts. The instructor then demonstrates the factoring process through three examples, using the X game and prime factorization techniques. Each example is broken down step-by-step, with explanations on how to identify and use common factors. The video concludes with a summary and information on additional resources and future video requests.

What is the primary goal when factoring quadratic trinomials by grouping?

• To simplify the expression to its minimal form

• To apply the quadratic formula

• To find the roots of the quadratic equation

• To divide the trinomial into four terms for grouping

What is the first step in factoring by grouping?

• Break the middle term into two terms

• Create a factor tree for the target number

• Identify the coefficients A, B, and C

• Play the 'X' game to find two numbers

In the first example, what are the two numbers found that multiply to -30 and add to -1?

• -5 and -6

• 5 and -6

• -5 and 6

• 5 and 6

After factoring by grouping in the first example, what is the factored form of the expression?

• 3x^2 + 5(x - 2)

• (3x + 5)(x - 2)

• (x + 5)(3x - 2)

• x(3x + 5) - 2

In the second example, what is the product of AC?

• -15

• -30

• 15

• 30

What two numbers are used to replace the middle term in the second example?

• -3 and -5

• 3 and 5

• -3 and 5

• 3 and -5

What is the final factored form in the second example?

• (k + 3)(5k - 1)

• (5k - 3)(k + 1)

• (k - 3)(5k + 1)

• (5k + 3)(k - 1)

In the third example, what is the value of AC?

• 60

• -40

• -60

• 40

Which pair of numbers replaces the middle term in the third example?

• 4 and 15

• -4 and -15

• -4 and 15

• 4 and -15

What is the factored form of the expression in the third example?

• (y - 4)(3y - 5)

• (y + 4)(3y + 5)

• (3y - 4)(y - 5)

• (3y + 4)(y + 5)