Can you help me with long division of the polynomials?

Yes I can

The steps are the same with integer long division: divide, multiply, subtract, repeat. Any remainder at the end is the numerator of a fraction with the divisor as the denominator (5 / 2 = 2 R 1 or 2 1/2)

I'll do the first one, the others follow the same pattern with different values.

. . . . ____________
x - 5 ) 4x² - 18x + 4

First step, divide: 4x² / x = 4x. Next multiply: 4x(x - 5) = 4x² - 20x. That gets written under the 4x² - 18x and then you subtract, carrying everything else over:

. . . . _4x___________
x - 5 ) 4x² - 18x + 4
. . . . . 4x² - 20x
. . . . ----------------
. . . . . . . . . . 2x + 4

Now we repeat: 2x / x = 2, 2(x - 5) = 2x - 10, then we subtract to get remainder:

. . . . _4x_+_2________
x - 5 ) 4x² - 18x + 4
. . . . . 4x² - 20x
. . . . ----------------
. . . . . . . . . . 2x + 4
. . . . . . . . . . 2x - 10
. . . . . . . . . --------------
. . . . . . . . . . . . . . 14

So the answer is:

4x + 2 + 14/(x - 5)