Factoring Expressions and Their Properties

The video tutorial explains how to factor the expression 4y^2 + 4y - 15 using the method of grouping. It begins by identifying that the leading coefficient is not 1 and explores the possibility of factoring by grouping. The tutorial then finds two numbers whose product is -60 and sum is 4, using the difference in their absolute values as a clue. After listing the factors of 60, the video identifies 6 and 10 as suitable numbers. Finally, the expression is broken down and factored by grouping, resulting in the factors (2y - 3) and (2y + 5).

What is the first step in factoring the expression 4y squared plus 4y minus 15?

• Use the quadratic formula

• Factor out a common term

• Complete the square

• Factor by grouping

What is the product of the two numbers we are looking for in the factoring process?

• 60

• -60

• 15

• -15

Why must the two numbers have different signs?

• Because their product is positive

• Because their sum is positive

• Because their product is negative

• Because their sum is negative

What is the significance of the difference in absolute values of the two numbers?

• It should be equal to the sum of the numbers

• It should be equal to the product of the numbers

• It should be equal to the leading coefficient

• It should be equal to the sum of the original expression's coefficients

Which pair of factors of 60 is suitable for factoring the expression?

• 1 and 60

• 5 and 12

• 6 and 10

• 2 and 30

What should be the sum of the two numbers used in the factoring process?

• -10

• 10

• -4

• 4

What is the next step after identifying the numbers 6 and 10?

• Divide the original expression by these numbers

• Multiply them together

• Add them to the original expression

• Break up the middle term using these numbers

What common factor is taken out from the first group of terms?

• 2y

• 3y

• 5y

• 4y

What common factor is taken out from the second group of terms?

• 6

• 5

• 3

• 2

What is the final factored form of the expression?

• (2y - 3)(2y + 5)

• (2y + 5)(2y + 3)

• (2y + 3)(2y - 5)

• (2y - 5)(2y + 3)