Ibuki factored 12x^7as (4x^3)(3x^4)
Melodie factored 12x^7as (2x^6) (6x).
Which of them factored 12x^7correctly?
Choose 1
A. Only Ibuki
B. Only Melodie
C. Both Ibuki and Melodie
D. Neither Ibuki nor Melodie

Both are correct.

Step-by-step explanation:

The key understanding here is that you can factor a monomial in many different ways!

To check if any of the factorizations is correct, we can multiply the factors and see if their product is really 12x^712x

7

12, x, start superscript, 7, end superscript.

Hint #22 / 4

\begin{aligned} (\blueD{4}\maroonD{x^3})(\blueD{3}\maroonD{x^4})&=(\blueD{4})(\blueD{3})(\maroonD{x^3})(\maroonD{x^4}) &=\blueD{12}\maroonD{x^7} \end{aligned}

(4x

3

)(3x

4

)

=(4)(3)(x

3

)(x

4

)

=12x

7

So Ibuki is correct!

Hint #33 / 4

\begin{aligned} (\blueD{2}\maroonD{x^6})(\blueD{6}\maroonD{x})&=(\blueD{2})(\blueD{6})(\maroonD{x^6})(\maroonD{x}) &=\blueD{12}\maroonD{x^7} \end{aligned}

(2x

6

)(6x)

=(2)(6)(x

6

)(x)

=12x

7

So Melodie is also correct!

Both Ibuki and Melodie are correct.