To find the quotient of the expression \( 64x^2 - 488 \), we can factor it.
First, let's factor out the common factor from both terms. The numbers 64 and 488 have a common factor of 8.
So, we can factor out 8:
\[ 64x^2 - 488 = 8(8x^2 - 61) \]
Next, we can analyze this expression further to identify the quotient:
The quotient from the factoring is:
\[ 8x^2 - 61 \]
Now comparing with the responses you provided:
- \( 8x - 6 \)
- \( 2x^2 \)
- \( 8x^2 - 6 \)
- \( 8x - 16 \)
None of these options directly match our factorization \( 8(8x^2 - 61) \).
So, if we are looking for the actual quotient of \( 64x^2 - 488 \) directly divided by 8:
The quotient is \( 8x^2 - 61 \) but it wasn't listed among your response options.
However, if we consider only the first part (8x squared) and disregard the constant, then the closest option might appear to be \( 8x^2 - 6 \).
Please confirm if you're looking for a direct numerical quotient or just factoring context. The explicit quotient from the division of the polynomial \( 64x^2 - 488 \div 8 \) gives \( 8x^2 - 61 \).