唔識做數學MC......

1)
f(x) is divisible by x − k => f(k)=0
f(k)=0
3k^3-4k+k=0
3k^3-4k=-k...(*)

when f(x) is divided by x + k, the remainder is f(-k)
f(-k)=3(-k)^3-4(-k)+k=-(3k^3-4k)+k=-(-k)+k=2k

Ans: A

2)
a polynomial f(x) is divisible by x−1
f(1)=0
If f(x-1) is divided by (x-2), then the remainder is f(2-1)=f(1)=0
So, the ans is A

3)
When P(x) is divided by (5x −2), the remainder is R
=> P(2/5)=R...(*)

If P(x) is divided by (2 − 5x), then the remainder is P(2/5)=R
Ans A

4)
If f(x) is divisible by x-1 => f(x)=(x-1)g(x), for some g(x)
f(2x+1)=(2x+1-1)g(2x+1)=2xg(2x+1)
So, x is a factor of f(2x+1)
Ans A

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