To demonstrate that you can divide polynomials by recognizing division as the inverse operation of multiplication, we want to find an equation that illustrates this relationship.
The expression \(\frac{8x^2 - 4x + 12}{4x}\) can be rewritten using multiplication.
The correct response that shows this relationship is:
\[ \frac{8x^2 - 4x + 12}{4x} = \left( \frac{1}{4x} \right)(8x^2 - 4x + 12) \]
So, the correct option is:
Start Fraction 8 x squared minus 4 x plus 12 over 4 x End Fraction equals left parenthesis Start Fraction 1 over 4 x End Fraction right parenthesis left parenthesis 8 x squared minus 4 x plus 12 right parenthesis.
This demonstrates that you can think of division as multiplying by the reciprocal, which is a key concept in polynomial division.
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