### Instruction: Find the equation of the oblique asymptote of the graph of
\[y = \frac{4x^2 - 10x + 7}{2x - 5}.\]Enter your equation in the form "$y = mx + b$".### Response: I know that an oblique asymptote is a line that the graph of the function approaches as x goes to infinity or negative infinity.
To find it, I need to use polynomial long division or synthetic division to divide the numerator by the denominator.
I'll use long division, and I'll write the denominator as $2x - 5 + 0$.
I'll start by asking what do I need to multiply $2x$ by to get $4x^2$.
The answer is $2x$, so I'll write that above the quotient line and multiply it by $2x - 5 + 0$ and write the result under the numerator.
I get $4x^2 - 10x + 0$.
I'll subtract that from the numerator and bring down the next term, which is $7$.
I get $0x^2 + 0x + 7$.
Now I ask what do I need to multiply $2x$ by to get $0x^2$.
The answer is $0$, so I write that above the quotient line and multiply it by $2x - 5 + 0$ and write the result under the remainder.
I get $0x^2 + 0x + 0$.
I subtract that from the remainder and get $0x^2 + 0x + 7$.
This is the final remainder, and it is nonzero, so I write it over the denominator and add it to the quotient.
The quotient is $2x + 0 + \frac{7}{2x - 5}$.
This means that as x goes to infinity or negative infinity, the fraction $\frac{7}{2x - 5}$ becomes very small and approaches zero.
So the graph of the function approaches the line $y = 2x + 0$ as x goes to infinity or negative infinity.
This is the equation of the oblique asymptote.