Someone please help me answer this math question. (Picture above)

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

step-by-step explanation: