Lina’s Solution Josh’s Solution
2 factor trees. Alina's factor tree of 126. 126 branches to 3 and 42. 42 branches to 6 and 7. 6 branches to 2 and 3. The equation is 126 = 2 times 3 squared times 7. Josh's factor tree of 126. 126 branches to 2 and 63. 63 branches to 9 and 7. The equation is 126 = 2 times 7 times 9.
Which statement explains the accuracy of the students’ work?
Lina’s solution is correct because it expresses 126 as a product of prime factors.
Josh’s solution is correct because the factor tree of every even number must begin with 2 and its factor pair.
Both solutions are correct because they both express 126 as a product of factors.
Neither solution is correct because the factor tree should have begun with 6 and 21.
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The accurate statement regarding the students' work is:
Lina’s solution is correct because it expresses 126 as a product of prime factors.
Lina correctly factorized 126 into its prime factors: \(126 = 2 \times 3^2 \times 7\), while Josh's solution is incorrect because he ended with \(9\) (which is not a prime factor) instead of breaking it down further into \(3 \times 3\). Thus, only Lina's prime factorization correctly represents the factors of 126.
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