Triple time unanswered algebra polynomial problem help

Please Perform the indicated division.
4x^3-8x^2+11x-4/x^2-3x

The problem asks me to divide the two polynomials NOT by factoring, please help me, I wasn't able to do it. I asked this question 3 times and no one seems to be answering, please help

It is the first time I see the question.

Let me rewrite it to make it clear.

(4x^3 - 8x^2 + 11x - 4) / (x^2 - 3x)

I will use a 4-step iterative process that works every time. However it is a bit long.
(iterative = a loop that you repeat until you are finished).

step 1:
Divide the highest-degree term in the numerator (4x^3) by the highest-degree term of the denominator (x^2)
4x^3 / x^2 = 4x

step 2:
multiply this by the denominator
4x(x^2 - 3x) = 4x^3 - 12x^2

step 3: subtract this from the numerator (careful with signs!)
(4x^3 - 8x^2 + 11x - 4) - (4x^3 - 12x^2) =
4x^3 - 8x^2 + 11x - 4 - 4x^3 + 12x^2 = 4x^2 + 11x - 4

step 4:
summarize what you have so far:
(4x^3 - 8x^2 + 11x - 4) / (x^2 - 3x) = 4x, with a remainder of 4x^2 + 11x - 4

Repeat the loop, using the remainder as the new numerator:

(4x^2 + 11x - 4) / (x^2 - 3x)

1:
4x^2 / x^2 = 4

2:
4(x^2 - 3x) = 4x^2 - 12x

3:
4x^2 + 11x - 4 - (4x^2 - 12x)
4x^2 + 11x - 4 - 4x^2 + 12x = 23x - 4

4:
(4x^3 - 8x^2 + 11x - 4) / (x^2 - 3x) = 4x + 4, with a remainder of 23x - 4

The degree of the remainder is LESS than the degree of the denominator, so we stop
[we also stop when the remainder hits 0, but this did not happen this time]

Final answer:

4x + 4 + (23x-4)/(x^2-3x)

long division

...4x³-8x^2+11x-4.....|..x² -3x
..............................|. 4x + 4
..-4x³+12x²
-----------------------
...0...+4x²+11x
........-4x² +12x
----------------------
.........0......23x-4 ..<------remainder

f(x)= 4x+4 +(23x-4)/(x²-3x)

..............................4x + 4
..............__________________
x^2 - 3x | 4x^3 - 8x^2 + 11x - 4
................4x^3 - 12x^2
...............____________
............................4x^2 + 11x - 4
............................4x^2 - 12x
............................__________…
......................................… 23x - 4

So, 4x+ 4 remainder 23x -4