F4 MTH POLYNOMIALS

👨🏻‍🏫 學術台數學

[匿名]

2010-01-26 5:48 am

When ax³ + 4x² +5x - 3 is divided by 2x² + x+ 1, the quotient and the remainder are x+b and cx-d respectively. Find the values of a, b, c, d.

更新1:

姐係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, d.

更新2:

thz a lot!!!!!

回答 (2)

用戶9112

2010-01-26 6:02 am

✔ 最佳答案

ax^3 + 4x^2 + 5x – 3 = (2x^2 + x + 1)(x + b) + (cx – d)
= 2x^3 + x^2 + x + 2bx^2 + bx + b + cx – d
= 2x^3 + (1 + 2b)x^2 + (1 + b + c)x + (b – d)
By comparing coefficients,
a = 2
4 = 1 + 2b => b = 3/2 (1.5)
5 = 1 + b + c => c = 4 – b => c = 5/2 (2.5)
-3 = b – d => d = 3/2 + 3 => d = 9/2 (4.5)

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用戶7639

2010-01-26 6:25 am

Alternative Solution

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