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Will factored [tex]7x^{6}[/tex] as [tex](3x^{2})(4x^{4})[/tex]. Olivia factored [tex]7x^{6}[/tex] as [tex](7x^{2})(x^{3})[/tex]. Which of them factored [tex]7x^{6}[/tex] correctly?

Answer :

To determine who factored [tex]7x^{6}[/tex] correctly, we need to verify each of the factorizations provided:

  1. 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.

  2. 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].

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