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Answer :
To determine who factored the expression [tex]\(7x^6\)[/tex] correctly, let's break down each person's factorization step-by-step.
Original Expression: [tex]\(7x^6\)[/tex]
1. Will's Factorization:
- Will factored [tex]\(7x^6\)[/tex] as [tex]\((3x^2)(4x^4)\)[/tex].
- First, look at the coefficients: [tex]\(3 \times 4 = 12\)[/tex]. So, he changed the original coefficient, which was 7. This is incorrect.
- Next, look at the exponents: [tex]\(2 + 4 = 6\)[/tex]. This part is fine since the sum of the exponents is correct.
2. Olivia's Factorization:
- Olivia factored [tex]\(7x^6\)[/tex] as [tex]\((7x^2)(x^3)\)[/tex].
- Check the coefficients: [tex]\(7 \times 1 = 7\)[/tex]. The original coefficient stays the same, which is correct.
- Check the exponents: [tex]\(2 + 3 = 5\)[/tex]. This part is incorrect because the sum of the exponents doesn't add up to 6.
After evaluating both factorizations, neither Will nor Olivia factored the expression [tex]\(7x^6\)[/tex] entirely correctly.
Therefore, the correct answer is:
(D) Ni Will ni Olivia
Original Expression: [tex]\(7x^6\)[/tex]
1. Will's Factorization:
- Will factored [tex]\(7x^6\)[/tex] as [tex]\((3x^2)(4x^4)\)[/tex].
- First, look at the coefficients: [tex]\(3 \times 4 = 12\)[/tex]. So, he changed the original coefficient, which was 7. This is incorrect.
- Next, look at the exponents: [tex]\(2 + 4 = 6\)[/tex]. This part is fine since the sum of the exponents is correct.
2. Olivia's Factorization:
- Olivia factored [tex]\(7x^6\)[/tex] as [tex]\((7x^2)(x^3)\)[/tex].
- Check the coefficients: [tex]\(7 \times 1 = 7\)[/tex]. The original coefficient stays the same, which is correct.
- Check the exponents: [tex]\(2 + 3 = 5\)[/tex]. This part is incorrect because the sum of the exponents doesn't add up to 6.
After evaluating both factorizations, neither Will nor Olivia factored the expression [tex]\(7x^6\)[/tex] entirely correctly.
Therefore, the correct answer is:
(D) Ni Will ni Olivia
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