Answer :
To determine who factored [tex]7x^{6}[/tex] correctly, we need to verify each of the factorizations provided:
Will's Factorization:
Will attempted to factor [tex]7x^{6}[/tex] as [tex](3x^{2})(4x^{4})[/tex].
First, let's multiply [tex]3x^{2}[/tex] and [tex]4x^{4}[/tex]:
[tex]3x^{2} \times 4x^{4} = 12x^{6}.[/tex]
This result, [tex]12x^{6}[/tex], is not equal to [tex]7x^{6}[/tex]. Therefore, Will's factorization is incorrect.
Olivia's Factorization:
Olivia factored [tex]7x^{6}[/tex] as [tex](7x^{2})(x^{3})[/tex].
Now, let's multiply [tex]7x^{2}[/tex] and [tex]x^{3}[/tex]:
[tex]7x^{2} \times x^{3} = 7x^{5}.[/tex]
However, this result is [tex]7x^{5}[/tex], not [tex]7x^{6}[/tex], which also means Olivia's factorization is incorrect.
Upon reviewing both factorizations, neither Will nor Olivia factored [tex]7x^{6}[/tex] correctly.
To correctly factor [tex]7x^{6}[/tex], you should look for factors whose product gives [tex]7x^{6}[/tex]. One simple and often correct factoring would be [tex](7x^{3})(x^{3})[/tex]. Let's verify:
Multiply these factors:
[tex]7x^{3} \times x^{3} = 7x^{6}.[/tex]
This correctly multiplies to the original expression [tex]7x^{6}[/tex].
