Answer:
the second answer option
Explanation:
it is similar to dividing 2 numbers.
2x³ + x² - 2x + 8 ÷ x + 2 =
first : what is 2x³/x ?
that's easy, right ? it is 2x².
now we need to multiply (x + 2) by 2x² and subtract this from the left side. and then pull down the next term :
2x³ + x² - 2x + 8 ÷ x + 2 = 2x²
- 2x³ + 4x²
---------------
0 - 3x² - 2x
now we need to find -3x²/x.
and that is ?
right : -3x
and again, we multiply (x + 2) by -3x, subtract this from the current left side and pull down the next term :
2x³ + x² - 2x + 8 ÷ x + 2 = 2x² - 3x
- 2x³ + 4x²
---------------
0 - 3x² - 2x
- - 3x² - 6x
---------------------
0 + 4x + 8
now we need to find 4x/x.
and that is 4.
and again, multiply (x + 2) by 4, subtract this from the current left side and pull down the next term, if there is one. if there is none left, we are finished :
2x³ + x² - 2x + 8 ÷ x + 2 = 2x² - 3x + 4
- 2x³ + 4x²
---------------
0 - 3x² - 2x
- - 3x² - 6x
---------------------
0 + 4x + 8
- 4x + 8
--------------------------
0 0 finished
and the result is : 2x² - 3x + 4
if there would be anything left at the bottom that is not 0, say for example 15, then the result would be
2x² - 3x + 4 + 15/(x+2).
but in this case the division is clean and without remainder.