急! F4數二題唔識做 10q21 06q29

1.
P = 9(x - 1)²
Q = ?
R = 15(x - 1)³(x + 1)(x - 2)²

H.C.F = 3
3 must be a factor Q.
5, 9 or (x - 1) must NOT be a factor of Q.

L.C.M. = 45(x - 1)³(x + 1)²(x - 2)²
(x + 1), (x - 2) or (x - 2)² MAYbe a factor of Q.

Two possible polynomials of Q : 3(x +1), 3(x - 2)


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2.
(a)
Let f(x) = x^2008 + 3

The remainder of f(x) ÷ (x+ 1)
= f(-1)
= (-1)^2008 + 3
= 4

(b)
Put x = 6 :
The remainder of (6^2008 + 3) ÷ 7is 4.
Then after (6^2008 + 3) days, it is 4 days after Saturday.
(Sunday, Monday, Tuesday, Wednesday)
Hence, it is Wednesday.