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