What is the quotient of (x3 + 3x2 + 5x + 3) ÷ (x + 1)?

the quotient is    1 x^2  +  2 x  +  3

Step-by-step explanation:

Use synthetic division here; it's less work.  Setting up synthetic division, we get:

-1        /        1         3          5          3

                             -1          -2        -3

                    1         2          3         0

Since the remainder is 0, we know that x + 1 divides evenly into x^3 + 3x^2 + 5x + 3 and that the quotient is    1 x^2  +  2 x  +  3