Explanation:
it is very similar to do the manual division of numbers.
5x² - 18x - 15 ÷ x - 4 =
so, we are starting on the left, dividing 5x² by x.
5x²/x = 5x
5x² - 18x - 15 ÷ x - 4 = 5x
then we multiply (x - 4) by 5x and subtract the result from the left part. and then we pull down the next term
5x² - 18x - 15 ÷ x - 4 = 5x
- 5x² -20x
---------------
0 2x - 15
and again, we take the left term and divide by x :
2x/x = 2
5x² - 18x - 15 ÷ x - 4 = 5x + 2
and again we multiply (x - 4) by 2 and subtract the result. and, if there still is one, we pull down the next term.
5x² - 18x - 15 ÷ x - 4 = 5x + 2
- 5x² -20x
---------------
0 2x - 15
- 2x - 8
--------------------
0 -7
there is no more term to pull down, so we are finished.
there is a remainder in the last line unequal to 0.
this becomes therefore -7/(x - 4).
so, the total result is
(5x² - 18x - 15) ÷ (x - 4) = 5x + 2 - 7/(x - 4)
2.
the same thing. we are now dividing the left terms by 3x, and then multiply that result every time with (3x - 2), subtract this abd pull the next term down until there is no more term to be pulled.
6x³ - 16x² + 17x - 6 ÷ 3x - 2 = 2x² - 4x + 3
- 6x³ - 4x²
---------------
0 -12x² + 17x
- -12x² + 8x
-----------------------
0 9x - 6
- 9x - 6
----------------------------
0 0
there is no remainder in the last line, so the result is
(6x³ - 16x² + 17x - 6) ÷ (3x - 2) = 2x² - 4x + 3