when a polynomial f(x) is divided by x+2 and x+3, the remainders are 11 and 6
respectively. find the remainder when f(x) is divided by (x+2)(x+3).
詳細步驟!!!!!!!!!!!!!
polynomial!!!!!!!
2010-02-21 6:24 am
回答 (2)
2010-02-21 7:25 am
✔ 最佳答案
依題意f(x)=(x+2)Q1(x)+11f(x)=(x+3)Q2(x)+6
故可設f(x)=(x+2)(x+3)Q(x)+k(x+2)+11
由f(-3)=6=-k+11得k=5
所以,所求餘式為5(x+2)+11即5x+21。
2010-02-21 6:41 am
Let f(x)=(x+2)(x+3)Q(x)+ax+b
f(-2)=11
-2a+b=11----(1)
f(-3)=6
-3a+b=6---(2)
(1)-(2): a=5
b=21
Hence remainder=(x+2)(x+3)
(when a polynomial is divided by g(x) with degree n,the degree of r(x) should be equal to or less than n-1,hence remainder should be expressed as ax+b)
2010-02-20 22:57:08 補充：
sorry,remainder=5x+21
f(-2)=11
-2a+b=11----(1)
f(-3)=6
-3a+b=6---(2)
(1)-(2): a=5
b=21
Hence remainder=(x+2)(x+3)
(when a polynomial is divided by g(x) with degree n,the degree of r(x) should be equal to or less than n-1,hence remainder should be expressed as ax+b)
2010-02-20 22:57:08 補充：
sorry,remainder=5x+21
收錄日期: 2021-04-23 20:41:25
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