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2012-02-16 7:23 am

29 (a) When x^3+7x^2+10x+a is divided by x+4 ,the quotient and the remiander are x^2+3x-2 and b respectively.Express b in terms of a.

(b) Hence,show that x^3+7x^2+10x-8 is divisible by x+4

30(a) When 8x^2+px+5 is divided by 4x+q,the quotient and the remiander are 2x+1 and 2 respectively.Fine the values of p and q.

回答 (1)

不用客氣

2012-02-16 9:13 am

✔ 最佳答案

29.
(a)
Dividend = Division * Quotient + Remainder
(x³ + 7x² + 10x + a) ÷ (x + 4) = x² + 3x - 2 ...... remainder = b
Hence, x³ + 7x² + 10x + a = (x + 4)(x² + 3x - 2) + b

Compare the constant terms on the both sides:
a = -8 + b
b = a + 8

(b)
In x³ + 7x² + 10x + a, when a = -8 :
b = (-8) + 8
b = 0

When x³ + 7x² + 10x - 8 is divided by x + 4, the remainder b = 0.
Hence, x³ + 7x² + 10x - 8 is divisible by x + 4.

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30.
(a)
Dividend = Division * Quotient + Remainder
(8x² + px + 5) ÷ (4x + q) = 2x + 1 ...... remainder = 2
Hence, 8x² + px + 5 = (4x + q)(2x + 1) + 2

Compare the constant terms on the both sides :
5 = q + 2
q = 3

Compare the x terms on the both sides :
px = 4x*1 + q*2x
px = 4x + 2qx
p = 4 + 2q
p = 4 + 2*3
p = 10

Hence, p = 10 and q = 3

參考: micatkie

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