Answer :
Final answer:
Neither Will nor Olivia factored 7x⁶ correctly. Will's attempt resulted in 12x⁶, and Olivia's attempt resulted in 7x⁵, both of which are not equal to the original expression 7x⁶. Therefore, the correct answer to the question is d.
Explanation:
The student's question is regarding the factoring of the expression 7x⁶. When factoring expressions, it's important to look for common factors that can be distributed across the terms.
Based on the properties of exponents, specifically that (xʳ)b = xa.b, one can factor out terms from an expression as long as the product of the exponents equals the original exponent.
In this case, Olivia factored 7x⁶ into (7x²)(x³). If we apply the exponent rule of multiplication, the result is:
(7x²) × (x³) = 7⁶ × x2+3 = 7x⁵.
This result is clearly incorrect because we started with 7x⁶, not 7x⁵. Therefore, Olivia's factorization is not accurate.
Let's check Will's factorization: he factored 7x⁶ as (3x²)(4x⁴). Again, applying the power rule of exponents, we would get:
(3x²) × (4x⁴) = 12x2+4 = 12x⁶.
Since the coefficient 12 does not equal the original coefficient 7, Will's factorization is also incorrect.
Therefore, the correct answer to the question is d. Neither Will nor Olivia factored 7x⁶ correctly.
