中四數學-多項式
2011-02-04 7:45 pm
When a polynomial p(x) is divided by x-1 and x+1,the remainders are 1 and 3 respectively.Find the remainder when p(x) is divided by x^2-1.
回答 (2)
2011-02-04 7:52 pm
✔ 最佳答案
Let p(x) = Q(x)(x^2 - 1) + (ax + b) = Q(x)(x - 1)(x + 1) + (ax + b)Sub. x = -1 and 1 into p(x)
p(-1) = -a + b = 3
p(1) = a + b = 1
Solve the equations, a = -1, b = 2
So, the remainder is 2 - x
2011-02-04 7:58 pm
p(x) = f(x)(x-1) + 1
p(1) = 1
and
p(x)= f(x)(x+1) + 3
p(-1) = 3
let p(x) = q(x)(x^2-1) + ax + b
then
p(1) = a + b = 1..........(1)
p(-1) = -a + b = 3............(2)
solving (1) and (2), get
a= -1, b=2
so the remainder is -x+2
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