Question
Which of the following worked equations demonstrates that you can divide polynomials by recognizing division as the inverse operation of multiplication?
8x^2-4x+12/4x=(-1/4x)(8x^2-4x+12)
8x^2-4x+12/4x=(-4x)(8x^2-4x+12)
8x^2-4x+12/4x=(1/4x)(8x^2-4x+12)
8x^2-4x+12/4x=(4x)(8x^2-4x+12)
8x^2-4x+12/4x=(-1/4x)(8x^2-4x+12)
8x^2-4x+12/4x=(-4x)(8x^2-4x+12)
8x^2-4x+12/4x=(1/4x)(8x^2-4x+12)
8x^2-4x+12/4x=(4x)(8x^2-4x+12)
Answers
GPT-4o mini
To determine which equation demonstrates that you can divide polynomials by recognizing division as the inverse operation of multiplication, we want an equation where dividing the polynomial \( 8x^2 - 4x + 12 \) by \( 4x \) is represented as multiplying by the inverse of \( 4x \).
From your options, the correct approach is:
- The division can be expressed as:
\[
\frac{8x^2 - 4x + 12}{4x} = (1/(4x))(8x^2 - 4x + 12)
\]
This correctly shows division as the inverse of multiplication since it expresses the operation as multiplying by the reciprocal of \( 4x \).
So the correct equation is:
\[
8x^2 - 4x + 12/4x = (1/4x)(8x^2 - 4x + 12)
\]
From your options, the correct approach is:
- The division can be expressed as:
\[
\frac{8x^2 - 4x + 12}{4x} = (1/(4x))(8x^2 - 4x + 12)
\]
This correctly shows division as the inverse of multiplication since it expresses the operation as multiplying by the reciprocal of \( 4x \).
So the correct equation is:
\[
8x^2 - 4x + 12/4x = (1/4x)(8x^2 - 4x + 12)
\]