polynomial question[2]

Q.1
If a polynomial f(x) is divisible by x + 1 which of the following must be a factor of f(x-1) ?
A. x
B. x + 1
C. x + 2
D. x - 2
f(x)=(x+1)p(x)
f(x-1)=(x)p(x-1)
So x must be a factor of f(x-1)
The answer is A
Q.2
When polynomials f(x) and g(x) are divided by x + a , the remainders are both R . Which of the following expressions must have a factor x - a ?
A. f(x) + g(x)
B. f(x) - g(x)
C. f(-x) + g(-x)
D. f(-x) - g(-x)
f(x) and g(x) are divided by x + a the remainders are both R
f(x)=(x+a)p(x)+R
g(x)=(x+a)q(x)+R
So f(-x) - g(-x)=(a-x)(p(x)-q(x))=-(x-a)(p(x)-q(x))
must have a factor x - a
The answer is D



2008-02-11 23:09:36 補充：
因為冇抵消R