To divide the expression \( 28x^2 + 7x - 77x^2 \), we first need to combine like terms. The expression simplifies as follows:
\[ 28x^2 - 77x^2 + 7x = -49x^2 + 7x \]
Now, let's factor out the common terms. We can factor out \(-7x\):
\[ -7x(7x - 1) \]
To find the quotient, we need more context on what we are dividing by. However, if this is merely testing the ability to manipulate the expression, we can summarize the simplified expression as:
\[ -7x(7x - 1) \]
In case you meant to divide by some polynomial or number (there’s no divisor specified) and are looking for the quotient itself based on options given, the logical deduction doesn't fit. Please clarify if you need to divide by a specific term or other expression.
If you are asking for the general quotient without that divisor context, the expression simplifies to \(-49x^2 + 7x\).
However, none of the options listed seem to correspond directly to this simplified result, and further clarification is needed to resolve any specific division.