英文數學題3個,快 - Ans.fyi 參考答案

英文數學題3個,快

[匿名]

2010-11-23 5:48 am

4.
(a)When 2x^3+3x^2+px+q is divided by 2x^2+x+2 ,the quotient is x+1 and the remainder is x-2. Find the values of p and q.

(b)When 4x^3-2x^2+kx+3 is divided by 2x-1 , the remainder is 4. Find the value of k.

(c)By using the syntheticdivision,find the quotient and the remainder when 2x^3+1-3x^2+x^4 is divided by x+x^2-3.

回答 (1)

用戶2053

2010-11-26 9:52 am

✔ 最佳答案

a) 2x^3 + 3x^2 + px + q = (x + 1)(2x^2 + x + 2) + x - 2= 2x^3 + x^2 + 2x + 2x^2 + x + 2 + x - 2= 2x^3 + 3x^2 + 4x + 0Comparing coefficient :p = 4q = 0Alternative :That means when 2x^3+3x^2+px+q is divided by x+1 , the remainder is x-2 :
By remainder theorem :
- 2 + 3 - p + q = - 1 - 2
q - p = - 4Since the constant term of (2x^2 + x + 2)(x + 1) + x - 2 is 2*1 - 2 = 0.So q = 0 , p = 4
b)When 4x^3 - 2x^2 + kx + 3 is divided by 2(x - 1/2) , the remainder is 4.
When 4x^3 - 2x^2 + kx + 3 is divided by (x - 1/2) , the remainder is 4.
By remainder theorem :4(1/2)^3 - 2(1/2)^2 + k(1/2) + 3 = 44/8 - 2/4 + k/2 = 1k = 2
c) -1+3] 1 2 -3 0 1............-1...3.................-1 3......................1.-3
____________________..........1.1..-1.|.4.-2商式 x^2 + x - 1
餘式 4x - 2

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