Question

if both students are correct, why are their factored expressions different? evelyn used? as the common factor. diana used? as the common factor. evelyns answer: 6w + 30 = 3(2w + 10) 3(2w + 10)=3(2w)+3(10)=6w + 30 ✓ dianas answer: 6w + 30 = 6(w + 5) 6(w + 5)=6(w)+6(5)=6w + 30 ✓

Explanation:

Step1: Analyze Evelyn's factored form

Evelyn factored $6w + 30$ as $3(2w + 10)$. Here, the common - factor she used is 3.

Step2: Analyze Diana's factored form

Diana factored $6w+30$ as $6(w + 5)$. Here, the common - factor she used is 6.

Step3: Explain different factored expressions

Both are correct because factoring can be done in different ways as long as the expanded form of the factored expression equals the original expression. The greatest common factor of $6w + 30$ is 6, but we can also factor out a non - greatest common factor like 3.

Answer:

Evelyn used 3 as the common factor.
Diana used 6 as the common factor.