Question

Which of the following worked equations demonstrates that you can divide polynomials by recognizing division as the inverse operation of multiplication?(1 point)
Responses

8
x
2
−
4
x
+
12
4
x
=
(
4
x
)
(
8
x
2
−
4
x
+
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

8
x
2
−
4
x
+
12
4
x
=
(
1
4
x
)
(
8
x
2
−
4
x
+
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

8
x
2
−
4
x
+
12
4
x
=
(
−
1
4
x
)
(
8
x
2
−
4
x
+
12
)

Start Fraction 8 x squared minus 4 x plus 12 over 4 x End Fraction equals left parenthesis negative Start Fraction 1 over 4 x End Fraction right parenthesis left parenthesis 8 x squared minus 4 x plus 12 right parenthesis

8
x
2
−
4
x
+
12
4
x
=
(
−
4
x
)
(
8
x
2
−
4
x
+
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
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Answer 1

The second equation.

(8x^2 − 4x + 12) / (4x) = (1/(4x))(8x^2 − 4x + 12)

Reason: dividing by 4x is the same as multiplying by its reciprocal 1/(4x). (You can also simplify termwise to 2x − 1 + 3/x.)