Factoring Quadratic Expressions

The video tutorial explains how to factor the quadratic expression r^2 + 4r - 45 by grouping. It begins by identifying two numbers whose product is -45 and sum is 4. After testing various combinations, the numbers -5 and 9 are found to work. The expression is then broken into terms using these numbers, and the terms are grouped and factored to achieve the final result.

What is the initial expression that needs to be factored?

• r^2 - 4r - 45

• r^2 + 4r + 45

• r^2 + 4r - 45

• r^2 - 4r + 45

Which method is chosen to factor the expression?

• Synthetic division

• Using the quadratic formula

• Factoring by grouping

• Completing the square

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

• -4

• 4

• -45

• 45

What is the sum of the two numbers we are looking for?

• -9

• -4

• 4

• 9

Which pair of numbers satisfies both the product and sum conditions?

• 5 and 9

• -5 and 9

• 5 and -9

• -5 and -9

How is the term 4r broken down using the identified numbers?

• 9r + 5r

• -5r + 9r

• 9r - 5r

• 5r + 9r

What common factor is factored out from the first group?

• 9

• 45

• -5

• r

What common factor is factored out from the second group?

• 45

• -5

• 9

• r

What is the common binomial factor in both groups?

• r - 5

• r - 9

• r + 9

• r + 5

What is the final factored form of the expression?

• (r - 9)(r - 5)

• (r - 5)(r + 9)

• (r + 9)(r + 5)

• (r + 5)(r - 9)