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1. Calculate the remainder when is divided by .

2. Given that and have the same remainder when divided by , find the possible values of a.

3. The expression leaves a remainder of and when divided by and respectively. Calculate the value of a and b.

[bg_collapse view=”link” color=”#22A609″ expand_text=”hint” collapse_text=”close hint” ]f (–2) = 19, f (1) = –8, 解联立[/bg_collapse]
4. The expression leaves a remainder of k when divided by and a remainder of when divided by . Show that .

[bg_collapse view=”link” color=”#22A609″ expand_text=”hint” collapse_text=”close hint” ]f (–2) = k, f (3) = 3k + 5，用代入消元法消掉k。[/bg_collapse]
5. A polynomial has a remainder 15 when divided by , and 9 when divided by . Find the remainder when is divided by .

[bg_collapse view=”link” color=”#22A609″ expand_text=”hint” collapse_text=”close hint” ]设, 则, 后解联立得a, b。余式为[/bg_collapse]
6. If deg , and f (x) is divided by, , , the remainders are , and respectively. Find .

[bg_collapse view=”link” color=”#22A609″ expand_text=”hint” collapse_text=”close hint” ]设, 则, 后解联立得, . 把, 代入[/bg_collapse]
7. where are constants. If satisfy the following conditions:

(i) when divided by , obtain the remainder ,

(ii) when divided by , we obtain the remainder .

Find the values of , and .
, 的值.
[bg_collapse view=”link” color=”#22A609″ expand_text=”hint” collapse_text=”close hint” ]从 (i) 可得 . 从 (ii) 可得. 代入可得，将 展开可得的值[/bg_collapse]

8. When the polynomial is divided by , , the remainder is and respectively. Find the remainder when is divided by .

[bg_collapse view=”link” color=”#22A609″ expand_text=”hint” collapse_text=”close hint” ]设, 可得。余式为[/bg_collapse]