What is the f of x over the g of x when f(x) = − 2x3 + x2 + 16x − 15 and g(x) = x + 3? −2x2 − 5x + 1 − 2x2 + 7x − 5 −2x2 + 7x − 5 − 12 over the quantity of x plus 3 − 2x2 − 5x + 1 − 12 over the quantity of x plus 3

− 2x3 + x2 + 16x − 15 and g(x) = x + 3.  Find f(x) / g(x).  
One way to do this is to use synthetic division.  Given the divisor (x+3), we decide that the divisor in synth. div. is -3.  Then:

       
-3   /   -2   +1    16     -15
                   6    -21     15
        
         -2      7     -5       0

Because there's no remainder, we can conclude that -3 is a root of the given function and (x+3) is a factor.  The coefficients of the quotient are

{-2, 7, -5), which works out to -2x^2 + 7x - 5.

Kindly use the symbol " ^ " for exponentiation:  x^2 Right
                                                                            x2  Wrong