Factoring Quadratics by Grouping Techniques

What is the first step in factoring expressions like 4y^2 + 4y - 15?

• Applying the quadratic formula

• Factoring by grouping

• Dividing the entire expression by the leading coefficient

• Finding two numbers that sum up to the middle coefficient

What product are we looking for with our two numbers in the context of factoring by grouping?

• The product of the leading coefficient and the constant term

• The sum of the leading coefficient and the constant term

• The difference between the leading coefficient and the constant term

• The quotient of the leading coefficient and the constant term

Which pair of numbers satisfies the conditions for our factoring problem?

• -6 and 10

• 5 and 12

• 6 and -10

• -5 and 12

What does the product of the two numbers need to equal in the context of this problem?

• 4

• -15

• 60

• -60

How do we rewrite the middle term using our identified numbers?

• By dividing the middle term equally

• By multiplying them with the leading coefficient

• As the sum of two terms with coefficients -6 and 10

• Using the quadratic formula

What is the purpose of breaking up the middle term in the process of factoring by grouping?

• To create groups for factoring

• To simplify the expression

• To identify the common factors

• To apply the quadratic formula

What common factor is factored out from the first group during the grouping process?

• -3

• 2y

• 5

• 10

What is the common factor factored out from the second group?

• 2y

• -3

• 5

• 10

After factoring out the common factors, what expression do we get?

• (2y + 3)(2y + 5)

• (2y - 3)(2y - 5)

• (2y + 3)(2y - 5)

• (2y - 3)(2y + 5)

What is the final factored form of 4y^2 + 4y - 15?

• (2y + 3)(2y + 5)

• (2y - 3)(2y - 5)

• (2y + 3)(2y - 5)

• (2y - 3)(2y + 5)