Factoring and Common Factors in Algebra

The video tutorial explains how to factor the expression 35k^2 + 100k - 15. It begins by identifying a common factor of 5, simplifying the expression to 5(7k^2 + 20k - 3). The tutorial then demonstrates factoring by grouping, breaking down the middle term into two parts, 21k and -1k, to facilitate grouping. The process involves finding two numbers whose product is -21 and sum is 20, leading to the factors 21 and -1. The expression is then grouped and factored into 5(k + 3)(7k - 1), completing the process.

What is the greatest common factor of the terms 35k^2, 100k, and -15?

• 3

• 5

• 7

• 10

After factoring out the greatest common factor, what is the new expression?

• 7k^2 + 20k - 3

• 5k^2 + 20k - 3

• 7k^2 + 15k - 3

• 5k^2 + 15k - 3

Which two numbers have a product of -21 and a sum of 20?

• 20 and 1

• 21 and -1

• 19 and 2

• 22 and -2

How is the term 20k rewritten using the numbers found?

• 20k - k

• 21k + k

• 21k - k

• 20k + k

What is the common factor in the first group of terms after rewriting?

• 3

• 7k

• 1

• k

What is the common factor in the second group of terms after rewriting?

• k

• 3

• -1

• 7k

What is the expression inside the parentheses after factoring out common factors from both groups?

• k - 3

• 7k + 3

• 7k - 3

• k + 3

What is the final factored form of the expression?

• 5(k + 3)(7k - 1)

• 5(k + 3)(7k + 1)

• 5(k - 3)(7k + 1)

• 5(k - 3)(7k - 1)

What is the purpose of factoring by grouping in this context?

• To make the expression easier to solve

• To find the roots of the equation

• To eliminate the variable

• To simplify the expression

Why is it important to verify the final factored form?

• To validate the original expression

• To confirm the factors are prime

• To check for calculation errors

• To ensure the expression is correct