To demonstrate that you can divide polynomials by recognizing division as the inverse operation of multiplication, you need to express the division in a way that relates it to multiplication.
From the options you provided, the correct representation would look like this:
\[ \frac{8x^2 - 4x + 12}{4x} = \left(\frac{1}{4x}\right)(8x^2 - 4x + 12) \]
This equation shows that dividing \(8x^2 - 4x + 12\) by \(4x\) is equivalent to multiplying \(8x^2 - 4x + 12\) by \(\frac{1}{4x}\), which illustrates division as the inverse of multiplication.
Thus, the corresponding response that correctly reflects this 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
3 answers