Synthetic division?

Question

Using synthetic division, find

a. the quotient
b. remainder, and
c. whether or not it's a function.

f(x) = 4x^4 - 15x^2 - 4
g(x) = x + 2

-----

So, c = -2. When I do the division, it should come out to 2 | 4 0 -15 0 -4.

Where do the zeros come from? How do I find the correct quotient? Please explain. Thanks.

Answer 1

-2|4__0__-15__0__- 4
_"|__- 8___16_-2___4
_"|4_- 8___1__-2___0

a) 4x³ - 8x² + x - 2
b) R = 0
c) quotient is a function as are f(x) and g(x)

Note
f(x) = 4x^4 + 0(x³) - 15(x²) + 0(x) - 4
is where zeros come from.