You have the following algebraic expression:
( 7x³ + 4x² - 2x + 1 )/(x + 1)
In order to simplify the previous expression you proceed as follow:
7x³ + 4x² - 2x + 1 | x + 1
-7x³ - 7x² 7x² - 3x + 1
0 - 3x² - 2x + 1
3x² + 3x
0 x + 1
-x - 1
0
Hence, the quotient of the given algebraic expression is:
( 7x³ + 4x² - 2x + 1 )/(x + 1) = 7x² - 3x + 1
The previous result is also the simplified form of the given expression