To demonstrate that you can divide polynomials by recognizing division as the inverse operation of multiplication, we need to find the correct expression for dividing \( 8x^2 - 4x + 12 \) by \( 4x \).
The correct division can be expressed as:
\[ \frac{8x^2 - 4x + 12}{4x} = \left(\frac{1}{4x}\right)(8x^2 - 4x + 12) \]
This shows that we are treating division as multiplying by the reciprocal.
Now, looking at your provided options, the correct equation is:
\[ \frac{8x^2 - 4x + 12}{4x} = \left(\frac{1}{4x}\right)(8x^2 - 4x + 12) \]
So the choice that corresponds to this equation in the response list 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 correctly illustrates that division can be understood as multiplying by the reciprocal.