Which of the following worked equations demonstrates that you can divide polynomials by recognizing division as the inverse operation of multiplication?(1 point) Responses 8x2−4x+124x=(14x)(8x2−4x+12) 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 8x2−4x+124x=(4x)(8x2−4x+12) Start Fraction 8 x squared minus 4 x plus 12 over 4 x End Fraction equals left parenthesis 4 x right parenthesis left parenthesis 8 x squared minus 4 x plus 12 right parenthesis 8x2−4x+124x=(−4x)(8x2−4x+12) Start Fraction 8 x squared minus 4 x plus 12 over 4 x End Fraction equals left parenthesis negative 4 x right parenthesis left parenthesis 8 x squared minus 4 x plus 12 right parenthesis 8x2−4x+124x=(−14x)(8x2−4x+12)

1 answer

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.