(x³ + 2x² - 3x + 2) ÷ (x + 1)

You need to review how to do long division.


            x² +  x - 4 + 
x + 1)x³ + 2x² - 3x + 2  
      x³ +  x²
            x² - 3x
            x² +  x
                -4x + 2
                -4x - 4
                      6

Answer: x² + x - 4 +  


To check:  Substitute 1 and 0 in original and in answer

Substitute 1 in the original:

(x³ + 2x² - 3x + 2) ÷ (x + 1)


((1)³ + 2(1)² - 3(1) + 2) ÷ ((1) + 1)

((1) + 2(1) - 3(1) + 2) ÷ ((1) + 1)

(1 + 2 - 3 + 2) ÷ (1 + 1)

              2 ÷ 2

                1

----------------------------------
Substitute 1 in answer:

x² + x - 4 + 

(1)² + (1) - 4 + 

1 + 1 - 4 + 

-2 + 

-2 + 3

  1
---------------------------

Substitute 0 in the original:

(x³ + 2x² - 3x + 2) ÷ (x + 1)

((0)³ + 2(0)² - 3(0) + 2) ÷ ((0) + 1)

((0) + 2(0) - 0 + 2) ÷ ((0) + 1)

(0 + 0 - 0 + 2) ÷ (0 + 1)

              2 ÷ 1

                2

----------------------------------
Substitute 0 in answer:

x² + x - 4 + 

(0)² + (0) - 4 + 

0 + 0 - 4 + 

-4 + 

-4 + 6

   2

---------------

So we get 1 when we substitute 1 in both the original
and the answer, and we get 2 when we substitute 0 in
both the original and the answer, so that shows that
this is very likely the correct answer.

Edwin