數學題

kuboy1314

YetSin 发表于 27-4-2015 06:45 AM
Q1: Functions f , g and h are defined by  f(x)= x/(x+1) , g(x)= (x+2)/x , h(x)= 3 + 2/x .[/backcol ...

新問題

Q1: When a polynomial p(x) (of degree,n >= 2) is divided by (2x - 1) , the remainder is 3/2 .When p(x) is divided by (x + 2), the remainder is -1 .Find the remainder when p(x) is divided by 2x^2 + 3x - 2.             (ans: x + 1)  看不懂題目...

Q2: Given the polynomial p(x) = x^5 - 3x^3 -2x^2 - 4x + 8 ,find the remainder when p(x) is divided by (x^2 - 4).Hence,find all the real roots of p(x).      (ans: 0;+-2,1)

Q3:
(a) Given that p(x)= x^2n - (m+2)x^2 + m + 1 , where n is a positive integer and m is a constant , show that x^2 - 1 is a factor of f(x) for all real values of m.      (ans: n=2)
(b) When m=8, (x-3) is a factor of p(x) . Find the value of n and factorise p(x) completely.               (ans: (x+3)(x-3)(x+1)(x-1))

Q4: The polynomial p(x) = x^4 + ax^3 - 7x^2 - 4ax + b has a factor x + 3 and when divided by x - 3 ,has remainder 60.
(a) Find the value of a and b.    (a=2,b=12)
(b) Factorise p(x) completely.       (x+3)(x-1)(x+2)(x-2)   這個地方希望你能詳細一些