Question

4 which student factored the expression correctly? evelyn diana both students neither student 4b evelyns answer: (6w + 30 = 3(2w + 10)) 4c dianas answer: (6w + 30 = 6(w + 5))

Explanation:

Step1: Check Evelyn's factorization

Expand $3(2w + 10)$: $3\times2w + 3\times10 = 6w + 30$. This matches the original expression, so Evelyn's factorization is mathematically valid, but not fully factored.

Step2: Check Diana's factorization

Expand $6(w + 5)$: $6\times w + 6\times5 = 6w + 30$. This also matches the original expression, and it is fully factored (the greatest common factor is used).

Step3: Evaluate correctness

Both factorizations are mathematically correct (they expand back to the original expression; full factorization is a stricter standard, but Evelyn's is still a valid partial factorization).

Answer:

C. Both students