Answer:
116
Step-by-step explanation:
If we assume the quotient is px³+qx²+rx+s
Then the following must hold:
(px³+qx²+rx+s)(x+1) + 14 = x⁴ + ax² - 16
From this we can establish p,q,r and s and then a. Do the multiplication, and then find that:
p=1
p+q=0
q+r=a
r+s=0
s+14=-16
Combine these, and get:
s = -30
r = 30
q = -1
a = 29
Now that we have a, we can do a normal factorization:
(x⁴ + 29x² - 16) = (x³ + 2x² + 33x + 66)·(x-2) + 116
