To use long division in polynomials, we follow steps similar to normal long division, but we look for the terms from higher degree to lower.
We are dividing:

By:

We want to multiply the divisor by some expression that will make the higher term equal to the higher term of the dividend. The higher term of the dividend is 4x³, to get to that, we can multiply the divisor by 2x²:

Now we have the same term, so we just substract what we have got from the dividend:

Notice that we don't have a third degree term anymore.
So, until now we have done:
- Multiplied the divisor by 2x²
- Got a remainder of -5x² + 3
Now, we just repeat with the remainder.
We want to multiply 2x - 1 so that the higher term is -5x², so we can multiply by -5x/2:

And we do the substraction:

So, now we have got:
- Multiplied the divisor by 2x² and then by -5x/2
- Got a remainder of -5x/2 + 3
Now, we repeat once more:
To get -5x/2, we multiply the divisor by -5/4:

And we substract from the remainder:

So, we have done:
- Multiplied the divisor by 2x² then -5x/2 then -5/4
- Got a remainder of 7/4
This means that th result of the division is:

And the remainder is:

But, the answer wants us to write what the dividend is equal to.
Let's write first in the division form:

Notice that we result is the quotient plus the remainder divided by the divisor.
If we multiply both sides by the divisor, we will get:

That is the answer.