1. When 2x^3-x^2+p is divided by x^2-qx+4, the quotient and the remainder are 2x+3 and 3-2x respectively. Find the values of p and q.
2. When x^3+ax^2-5x+9 is divided by x+4, the quotient and the remainder are x^2+bx-1 and 13 respectively. Find the values of a and b.
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唉..又係數學(Basic)
2010-04-01 5:46 am
回答 (3)
2010-04-01 6:25 am
✔ 最佳答案
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2010-03-31 22:25:48 補充：
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2010-04-01 6:44 am
2010-04-01 6:32 am
Basic Principle: When Y is divided by X, if the quotient is Q and the remainder is R, then Y = XQ + R.
Q1.
2x^3 - x^2 + p = (x^2 - qx + 4)(2x + 3) + (3 - 2x)
Comparing the coefficient of x^2 term
- x^2 = 3x^2 - 2qx^2
- 1 = 3 - 2q
2q = 4, q = 2.
Q2.
x^3 + ax^2 - 5x + 9 = (x + 4)(x^2 + bx - 1) + 13
Comparing the x^2 term,
ax^2 = 4x^2 + bx^2
a = 4 + b ...............(1)
Comparing coefficient of x term,
- 5x = 4bx - x
-5 = 4b - 1
so b = - 1
and a = 4 - 1 = 3. [ From (1)]
2010-03-31 22:34:42 補充：
For Q1, comparing the constant term, we get p = 15.
Q1.
2x^3 - x^2 + p = (x^2 - qx + 4)(2x + 3) + (3 - 2x)
Comparing the coefficient of x^2 term
- x^2 = 3x^2 - 2qx^2
- 1 = 3 - 2q
2q = 4, q = 2.
Q2.
x^3 + ax^2 - 5x + 9 = (x + 4)(x^2 + bx - 1) + 13
Comparing the x^2 term,
ax^2 = 4x^2 + bx^2
a = 4 + b ...............(1)
Comparing coefficient of x term,
- 5x = 4bx - x
-5 = 4b - 1
so b = - 1
and a = 4 - 1 = 3. [ From (1)]
2010-03-31 22:34:42 補充：
For Q1, comparing the constant term, we get p = 15.
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