Question

Consider the polynomial −4(34p−2n)+6n−(8n+p)%0D%0A−%0D%0A4%0D%0A(%0D%0A3%0D%0A4%0D%0A%0D%0A−%0D%0A2%0D%0A%0D%0A)%0D%0A+%0D%0A6%0D%0A%0D%0A−%0D%0A(%0D%0A8%0D%0A%0D%0A+%0D%0A%0D%0A)%0D%0A.%0D%0A%0D%0AWhich expression is equivalent to the given polynomial?%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A6n−3p%0D%0A6%0D%0A%0D%0A−%0D%0A3%0D%0A%0D%0A6 n minus 3 p%0D%0A%0D%0A6n−4p%0D%0A6%0D%0A%0D%0A−%0D%0A4%0D%0A%0D%0A6 n minus 4 p%0D%0A%0D%0A−10n−2p%0D%0A−%0D%0A10%0D%0A%0D%0A−%0D%0A2%0D%0A%0D%0Anegative 10 n minus 2 p%0D%0A%0D%0A−10−3p

Answer 1

Let's simplify the polynomial step by step:

The given polynomial is:

\[ -4(34p - 2n) + 6n - (8n + p) \]

1. Distribute \(-4\) through \((34p - 2n)\): \[ -4 \cdot 34p + -4 \cdot (-2n) = -136p + 8n \]

2. Replace the polynomial with the simplified expression: \[ -136p + 8n + 6n - (8n + p) \]

3. Combine like terms for \(n\):

   • Combine \(8n\) and \(6n\): \[ 8n + 6n = 14n \]

4. Now substitute back to get: \[ -136p + 14n - 8n - p \]

5. Combine \(-p\) with \(-136p\): \[ -136p - p = -137p \]

6. Combine \(14n - 8n\) for \(n\): \[ 14n - 8n = 6n \]

7. Therefore, the final expression we have is: \[ -137p + 6n \]

Now, we need to check against the responses given. None of the options seem to match the final expression of \(-137p + 6n\) exactly; thus, it is possible there could be an error in the provided options, or the polynomial might have been misinterpreted.

However, if the equivalent expressions use different coefficients, look for a polynomial with similar terms but with coefficients modified, like:

1. \(6n - 3p\)
2. \(6n - 4p\)
3. \(-10n - 2p\)
4. \(-10 - 3p\)

Since our result was \(-137p + 6n\), no option seems to be closely fit, confirming that the polynomial might not match the expected responses.

Are you looking for a further mathematical simplification, or is there anything specific you would like to clarify about this polynomial?