Answer:
Therefore, the quotient is 2x^2 - 2x + 7, and the remainder is 4. We can express the original expression as:
(2x^3 - 5x + 1) = (x + 1)(2x^2 - 2x + 7) + 4
Explanation:
To find the quotient of the polynomial expression (2x^3-5x+1) divided by (x+1), we will perform polynomial long division as follows:
2x^2 - 2x + 7
____________________
x + 1 | 2x^3 + 0x^2 - 5x + 1
- (2x^3 + 2x^2)
---------------
-2x^2 - 5x
+ (-2x^2) - 2x
------------
-3x + 1
- (-3x - 3)
---------
4
Therefore, the quotient is 2x^2 - 2x + 7, and the remainder is 4. We can express the original expression as:
(2x^3 - 5x + 1) = (x + 1)(2x^2 - 2x + 7) + 4