The remainder when f(x) is divided by x+1 is 0.
Using this result, find the remainder when f(x) is divided by x^2-1.
更新1:
Why is ax + b
f4數學題一問?f4數學題一問?
2011-09-18 12:23 am
Let f(x) = x^n+2x+3, where n is a positive odd integer.
The remainder when f(x) is divided by x+1 is 0.
Using this result, find the remainder when f(x) is divided by x^2-1.
The remainder when f(x) is divided by x+1 is 0.
Using this result, find the remainder when f(x) is divided by x^2-1.
回答 (2)
2011-09-18 1:07 am
✔ 最佳答案
Let f(x) = (x + 1)(x - 1)Q(x) + ax + bSince -1 is a root of f(x) => n is odd
f(-1) = 0 => b - a = 0
f(1) = 1 + 2 + 3 = 6 =>a + b = 6
So, a = b = 3
The remainder is 3x + 3
2011-09-18 3:44 am
Since by fundamental theorem,
deg R(x) < deg D(x)
Since D(x) = x^2 - 1 , which is deg 2.
Then, deg R(x) can be 1 or 0.
To suppose no losing of terms, ax + b is required for assuming the form of R(x)
deg R(x) < deg D(x)
Since D(x) = x^2 - 1 , which is deg 2.
Then, deg R(x) can be 1 or 0.
To suppose no losing of terms, ax + b is required for assuming the form of R(x)
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