If the polynomial `f(x)=a x^3+b x-c` is divisible by the polynomial `g(x)=x^2+b x+c` , then `a b=` (a) `1` (b) `1/c` (c) `-1` (d) `-1/c`

If x+1 is a factor of the polynomial 2x^2+k x , then k= (a) -2 (b) -3 (c) 4 (d) 2

If alpha,\ beta are the zeros of polynomial f(x)=x^2-p(x+1)-c , then (alpha+1)(beta+1)= (a) c-1 (b) 1-c (c) c (d) 1+c

If x^3-3x^2+3x+7=(x+1)(a x^2+b x+c),\ then a+b+c= (a)4 (b) 12 (c) -10\ (d) 3

If alpha,\ beta,\ gamma are the zeros of the polynomial f(x)=a x^3+b x^2+c x+d , then 1/alpha+1/beta+1/gamma= (a) b/d (b) c/d (c) -c/d (d) c/a

If alpha,\ beta are the zeros of the polynomial f(x)=x^2-p(x+1)-c such that (alpha+1)(beta+1)=0 , then c= (a) 1 (b) 0 (c) -1 (d) 2

Let f(x) be a polynomial such that f(-1/2)=0, then a factor of f(x) is:? (a) 2x-1 (b) 2x+1 (c) x-1 (d) x+1

Let P(x) and Q(x) be two polynomials.Suppose that f(x) = P(x^3) + x Q(x^3) is divisible by x^2 + x+1, then (a) P(x) is divisible by (x-1),but Q(x) is not divisible by x -1 (b) Q(x) is divisible by (x-1), but P(x) is not divisible by x-1 (c) Both P(x) and Q(x) are divisible by x-1 (d) f(x) is divisible by x-1

If a b c = 0, then ({(x^a)^b}^c)/({(x^b)^c}^a) = (a)3 (b) 0 (c) -1 (d) 1

If the remainder R(x)=ax+b is ontained by dividing the polynomial x^(100) by the polynomial x^(2)-3x+2 then (A) a=2^(100)-1 (B) b=2(2^(99)-1) (C) b=-2(2^(99)-1) (D) a=2^(100)

If f(x) and g(x) are two polynomials such that the polynomial h(x)=xf(x^3)+x^2g(x^6) is divisible by x^2+x+1, then f(1)=g(1) (b) f(1)=1g(1) h(1)=0 (d) all of these