F4 Maths Polynomials

2007-03-31 8:57 am
Question
When x^4 + ax^2 + b is divided by x^2 - x + 3, which of the following cannot be the remainder

A. 5
B. x +5
C. x - 3
D. x^2 + 4x - 1

Please show me the calculation steps and reasons
Thanks

回答 (1)

2007-03-31 9:03 am
✔ 最佳答案
D
The degree of x^2 + 4x -1 is 2, the largest exponent among all the terms of the polynomial.

The degree of the remainder must be straightly less than the degree of the quotient (x^2 - x + 3), which is 2, so A (degree 0), B (degree 1) and C (degree 1) are all possible, but not D.

2007-04-02 01:48:35 補充:
thanks for correcting my mistake


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