幾條f.4 polynomial

2010-03-05 3:07 am

30. when 2x^3-3x^2+ax+4 is divided by x^2+bx-2,the quotient and the remainder are 2x+3 and 12x+c respectively.find the values of a,b and c.

31. when ax^3+4x^2+5x-3 is divided by 2x^2 +x-1 ,the quotient and the
remainder are x+b and cx-d respectively.find the values of a,b,c and d.

32.when 3x^3-16x^2+ax+b is divded by (x-1)(x-3),the remaider is x+2.find the values of a and b.

回答 (1)

用戶10012

2010-03-05 3:31 am

✔ 最佳答案

30.
2x^3 - 3x^2 + ax + 4 = (x^2 + bx - 2)(2x + 3) + (12x + c)
Comparing coefficients we get
4 = (-2)(3) + c, so c = 10.
3b - 4 + 12 = a and
3 + 2b = - 3, so b = - 3 and a = 3(-3) - 4 + 12 = - 1.
31.
ax^3 + 4x^2 + 5x - 3 = (2x^2 + x - 1)(x + b) + (cx - d)
Comparing coefficients,
a = 2.
2b + 1 = 4 , so b = -3/2.
b - 1 + c = 5, so c = 6 - b = 6 + 3/2 = 15/2.
-b - d = - 3, so d = 3 - b = 3 + 3/2 = 9/2.
32.
3x^3 - 16x^2 + ax + b = (x - 1)(x - 3)Q(x) + (x + 2)
Put x = 1
3 - 16 + a + b = 3
a + b = 16....................(1)
Put x = 3
81 - 144 + 3a + b = 5
3a + b = 68...............(2)
(2) - (1) we get
2a = 52
a = 26.
b = 16 - a = - 10.

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