Answer :
Let's determine who factored [tex]\(7x^6\)[/tex] correctly between Will and Olivia.
### Will's Factorization:
Will's factorization is [tex]\((3x^2)(4x^4)\)[/tex].
1. Multiply the coefficients: [tex]\(3 \times 4 = 12\)[/tex].
2. Multiply the powers of [tex]\(x\)[/tex]: [tex]\(x^2 \times x^4 = x^{2+4} = x^6\)[/tex].
Therefore, Will's product would be [tex]\(12x^6\)[/tex].
### Olivia's Factorization:
Olivia's factorization is [tex]\((7x^2)(x^3)\)[/tex].
1. Multiply the coefficients: [tex]\(7 \times 1 = 7\)[/tex].
2. Multiply the powers of [tex]\(x\)[/tex]: [tex]\(x^2 \times x^3 = x^{2+3} = x^5\)[/tex].
Therefore, Olivia's product would be [tex]\(7x^5\)[/tex].
### Correct Factorization:
The original expression is [tex]\(7x^6\)[/tex]. For a product to be correct, it should multiply to [tex]\(7x^6\)[/tex].
- Will got [tex]\(12x^6\)[/tex], which does not match [tex]\(7x^6\)[/tex].
- Olivia got [tex]\(7x^5\)[/tex], which also does not match [tex]\(7x^6\)[/tex].
### Conclusion:
Since neither Will nor Olivia achieved the correct factorization, the answer is:
(D) Neither Will nor Olivia
### Will's Factorization:
Will's factorization is [tex]\((3x^2)(4x^4)\)[/tex].
1. Multiply the coefficients: [tex]\(3 \times 4 = 12\)[/tex].
2. Multiply the powers of [tex]\(x\)[/tex]: [tex]\(x^2 \times x^4 = x^{2+4} = x^6\)[/tex].
Therefore, Will's product would be [tex]\(12x^6\)[/tex].
### Olivia's Factorization:
Olivia's factorization is [tex]\((7x^2)(x^3)\)[/tex].
1. Multiply the coefficients: [tex]\(7 \times 1 = 7\)[/tex].
2. Multiply the powers of [tex]\(x\)[/tex]: [tex]\(x^2 \times x^3 = x^{2+3} = x^5\)[/tex].
Therefore, Olivia's product would be [tex]\(7x^5\)[/tex].
### Correct Factorization:
The original expression is [tex]\(7x^6\)[/tex]. For a product to be correct, it should multiply to [tex]\(7x^6\)[/tex].
- Will got [tex]\(12x^6\)[/tex], which does not match [tex]\(7x^6\)[/tex].
- Olivia got [tex]\(7x^5\)[/tex], which also does not match [tex]\(7x^6\)[/tex].
### Conclusion:
Since neither Will nor Olivia achieved the correct factorization, the answer is:
(D) Neither Will nor Olivia
