Question

Divide (3x^3+5x) by (x+3)

Answer 1

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