Remainder Theorem ကိုအသံုးခ်တြက္ေသာ ပုစာၦမ်ား(2)

Example 8

Given that the expression x3 - ax2 + bx + c leaves the same remainder when divided by x + 1 or x - 2 , find a in terms of b.
ေပးထားေသာ ကိန္းတန္း x3 - ax2 + bx + c ကို x + 1 ႏွင့္ x - 2 တို႔ျဖင့္စားေသအခါ တူညီေသာ အၾကြင္းရ၏။ a ၏ တန္ဖိုးကို b ပါ၀င္ေသာ ကိန္းတန္းျဖင့္ ေဖၚျပပါ။

http://i627.photobucket.com/albums/tt352/Thu-Rein/template/th_bluearrow.gif Let f(x) = x3 - ax2 + bx + c.
By the problem,
f(-1) = f(2)
(-1)3 - a(-1)2 + b(-1) + c = (2)3 - a(2)2 + b(2) + c
-1 - a -b = 8 - 4a + 2b
a = b + 3

Example 9

Given that the remainder when x3 - x2 + ax is divided by x + a where a>0, is twice the remainder when it is divided by x - 2a, find the value of a.
x3 - x2 + ax ကို x + a ႏွင့္စား၍ ရေသာ အၾကြင္းသည္ x - 2a ႏွင့္စား၍ ရေသာ အၾကြင္း၏ ၂ ဆျဖစ္လွ်င္ a ၏ တန္ဖိုးကို ရွာပါ။ (မွတ္ခ်က္ a>0)

http://i627.photobucket.com/albums/tt352/Thu-Rein/template/th_bluearrow.gif Let

By the problem,



Since a>0,