PP2 DS 129

[nemolee]

If t is a positive integer and r is the remainder when t^2 + 5t + 6 is divided by 7, what is the value of r ?
(1) When t is divided by 7, the remainder is 6.
(2) When t2 is divided by 7, the remainder is 1.

ANS: A

錯誤的選到了 E
我先用因式分解之下得 (t+2)(t+3)=0，可是還是找不出答案，選到了E

請問這題應該要從那邊開始「下手」

謝謝

[Huang Hsin-Yi]

t^2+5t+6=7a.......r 問r=?
(1)t= 7b+6 代入上式
(7b+6)^2+5(7b+6)+6=49b^2+84b+35B+72
therefore 72/7 r=2......sufficient

(2)t2=7c+1代入上式
(7c+1)+5t+6=7c+5t+7
5t/7 r=3,1,6............insufficient

[nemolee]

原來系要代入法... ><
記得了.. 謝謝. . . .