To find the quotient of \( 64x^2 - 488 \), we need to factor out the common factor.
First, identify the greatest common factor (GCF) of the coefficients 64 and 488.
- Find the GCF of 64 and 488:
- The prime factorization of 64 is \( 2^6 \).
- The prime factorization of 488 is \( 2^3 \times 61 \).
- The GCF of 64 and 488 is \( 8 \).
Now, we can factor out \( 8 \) from the expression:
\[ 64x^2 - 488 = 8(8x^2 - 61) \]
Now we have factored out 8, but the question asks for the quotient. To find the quotient when dividing \( 64x^2 - 488 \) by \( 8 \):
\[ \frac{64x^2 - 488}{8} = 8x^2 - 61 \]
However, none of the listed responses match this exact form.
If we need to choose the closest term from the provided responses, none are exact.
Nevertheless, if interpreting the responses based on common polynomial expressions, the closest could be approached but not equal. Therefore, none of the listed options are correct as presented.
In conclusion, the answer as factored is :
\( 8x^2 - 61 \), which is not present in your response options. Please double-check if the question is clarified.