Using synthetic division:
Draw an upside down division symbol. Place the constant of x + 3 (-3) on the outside, and the coefficients of 3x³ + 5x on the inside, like so:
| x³ x² x¹ x⁰
-3 | 3 0 5 0
|
|___________
Bring down the first coefficient:
| x³ x² x¹ x⁰
-3 | 3 0 5 0
|
|___________
3
Multiply the number outside the symbol (-3) by the 3 you've just brought down. Place that number under the next coefficient to the right.
| x³ x² x¹ x⁰
-3 | 3 0 5 0
| -9
|___________
3
Add the new number (-9) to the coefficient above it and place that number directly underneath it.
| x³ x² x¹ x⁰
-3 | 3 0 5 0
| -9
|___________
3 -9
Repeat this process until you've reach the end of the symbol.
| x³ x² x¹ x⁰
-3 | 3 0 5 0
| -9 27 -96
|___________
3 -9 32 -96
The resulting numbers are coefficients, the first three of the quotient, and the last one of the remainder. The remainder is the last coefficient (-96) over the divisor.
(3x^3+5x) / (x+3) = 3² - 9x + 32 + -96 / x + 3
