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# 唔識做數學MC......

Let f(x) = 3x^3 − 4x + k. If f(x) is divisible by x − k, find the remainder when f(x) is divided by x + k.

A. 2k

B. k

C. 0

D. -k

E. -k-1

If a polynomial f(x) is divisible by x − 1, then f(x − 1) is divisible by

A. x-2.

B. x+2.

C. x-1.

D. x+2.

E. x.

P(x) is a polynomial. When P(x) is divided by (5x −2), the remainder is R. If P(x) is divided by (2 − 5x), then the remainder is

A. R.

B. -R.

C. (2/5)R.

D. (2/5).

E. -(2/5).

Let f(x) be a polynomial. If f(x) is divisible by x-1, which of the following must be a factor of f(2x+1)?

A. x

B. x-3

C. 2x-1

D. 2x+1

Rating

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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