.
To get the answer, use the Remainder theorem.
The Remainder theorem states:
1. The remainder of division the polynomial 
by the binomial 
is equal to the value 
of the polynomial.
2. The binomial divides the polynomial if and only if the value of 
is the root of the polynomial , i.e. 
.
3. The binomial factors the polynomial if and only if the value of is the root of the polynomial , i.e. .
See the lesson
- Divisibility of polynomial f(x) by binomial x-a
in this site.
So, what you need to do is to check if the value (-1) is the root of the given polynomial. It is easy:
(-1)^900 - 3*(-1)^450 + 2*(-1)^225 + 4 = 1 - 3 + 2*(-1) + 4 = 1 - 3 - 2 + 4 = 0.
Answer. According to the Remainder Theorem, the binomial (x+1) is a divisor of the given polynomial.
Solved.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic
"Divisibility of polynomial f(x) by binomial (x-a). The Remainder theorem".
