[*f(x)=x^(4)-3x^(2)+4x+5],[g(x)=x^(2)+1-x]

Apply the division algorithm to find the quotient and remainder on dividing f(x)=x^4-3x^2+4x+5 by g(x)=x^2+1-x

f(x)=4x^(3)-12x^(2)+14x-3,g(x)=2x-1

f(x)=x^(3)+4x^(2)-3x+10,g(x)=x+4

" 2" f(x)=4x^(4)-3x^(3)-2x^(2)+x-7,g(x)=x-1

If p(x)=x^(5)+4x^(4)-3x^(2)+1 " and" g(x)=x^(2)+2 , then divide p(x) by g(x) and find quotient q(x) and remainder r(x).

If p(x)=x^(5)+4x^(4)-3x^(2)+1 " and" g(x)=x^(2)+2 , then divide p(x) by g(x) and find quotient q(x) and remainder r(x).

Identify polynomials in the following: f(x)=4x^(3)-x^(2)-3x+7g(x)=2x^(3)-3x^(2)+sqrt(x)-1p(x)=(2)/(3)x^(2)-(7)/(4)x+9q(x)=2x^(2)-3x+(4)/(x)+2h(x)=x^(4)-x^((2)/(3))+x-1f(x)=2+(3)/(x)+4x

Use the Factor Theorem to determine whether g(x) is factor of f(x) in each of the following cases : (i) f(x)=5x^(3)+x^(2)-5x-1, g(x)=x+1 (ii) f(x)=x^(3)+3x^(2)+3x+1,g(x)=x+1 (iii) f(x)=x^(3)-4x^(2)+x+6,g(x)=x-2 (iv) f(x)=3cx^(3)+x^(2)-20x+12,g(x)=3x-2 f(x)=4x^(3)+20x^(2)+33x+18,g(x)=2x+3

check whether p(x) is a multiple of g(x) or not (i) p(x) =x^(3)-5x^(2)+4x-3,g(x) =x-2. (ii) p(x) =2x^(3)-11x^(2)-4x+5,g(x)=2x+1