1)given that when a polynomial x^3 +2ax-b is divided by x-3 ,the remainder is 1.
Using this piece of information,write a polynomial of degree 3 in x which gives a
remainder b when it is divided by x-3.
2) when 6x^3 -13x^2 +px-5 is divided by 3x^2 -qx+1,the quotient and the remainder are 2x-1 and 3x+r respectively.Find the values of p,q and r
F.4 maths(polynomial)
2013-02-28 4:40 am
回答 (1)
2013-02-28 5:11 am
✔ 最佳答案
1)By remainder theorem , 3³ + 2a(3) - b = 1
3³ + 2a(3) - 1 = b
So x³ + 2ax - 1 gives a remainder b when it is divided by x-3.
2)6x³ - 13x² + px - 5 = (2x - 1)(3x² - qx + 1) + 3x + r
6x³ - 13x² + px - 5 = 6x³ - 2qx² + 2x - 3x² + qx - 1 + 3x + r
6x³ - 13x² + px - 5 = 6x³ - (2q + 3)x² + (q + 5)x + r - 1
Comparing coefficients :
2q + 3 = 13
q = 5p = q + 5 = 10r - 1 = - 5
r = - 4
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