Solve using synthetic division (show each step). (a3 +5a2 +14a+16)÷(a+2)

The quotient is 1x^2 + 3x + 8.

Step-by-step explanation:

First:  Please use " ^ " to denote exponentiation:  (a^3 +5a^2 +14a+16).

We are dividing this polynomial by (a + 2).  The equivalent divisor in synthetic division is -2.  We set up this synth. div. as follows:

-2    )    1    5    14    16

                -2    -6   -16

          1      3     8      0

Because the remainder is zero (0), we can safely assume that x  = -2 is a root of (a^3 +5a^2 +14a+16) and that x + 2 is a factor of  (a^3 +5a^2 +14a+16).

The quotient is 1x^2 + 3x + 8.