Factoring Expressions and Common Factors

The video tutorial explains how to factor an expression by grouping. It begins by discussing the lack of a common factor across all terms, necessitating grouping. The tutorial then demonstrates factoring the first group of terms, followed by the second group. Finally, it combines the factored groups into a single expression, highlighting the common factor and verifying the result.

Why can't the entire expression be factored by a single common factor?

• There is a common factor across all terms.

• Not all terms are divisible by the same variable.

• All terms are divisible by 5.

• The expression is already factored.

What common factors are identified in the first two terms?

• 5 and s

• 5 and r

• r and s

• 5 and 25

How is the expression 5rs + 25r rewritten?

• 5r(s + r)

• rs(5 + 25)

• 5s(r + 5)

• 5r(s + 5)

What common factor is used for the second pair of terms?

• Positive 3

• Negative 3

• Positive 5

• Negative 5

What is the result of factoring -3s - 15?

• -3(s + 5)

• 3(s - 5)

• 3(s + 5)

• -3(s - 5)

What common factor is identified in the new expression after grouping?

• r - 3

• 5r

• s - 5

• s + 5

How is the expression rewritten after factoring out the common factor?

• (s - 5)(5r - 3)

• (s - 5)(5r + 3)

• (s + 5)(5r - 3)

• (s + 5)(5r + 3)

What is the purpose of distributing the terms in the final step?

• To simplify the expression further

• To change the expression

• To verify the correctness of the factorization

• To find a new common factor

What is the result of distributing s + 5 in the final expression?

• An incorrect expression

• A simplified expression

• A new expression

• The original expression

What is the final factored form of the expression?

• s - 5 times 5r - 3

• s + 5 times 5r + 3

• s + 5 times 5r - 3

• s - 5 times 5r + 3