Factorize `x^(4)-2x^(3)-9x^(2)+2x+8` using remainder theorem.

Check if ( x+ 2) and ( x-4) are the sides of a rectangle whose area is x^(2) - 2x - 8 by using factor theorem.

Check whether , x - 2 is a factor of the polynomial x^3 - x^2 - 4 by using factor theorem .

Using the Factor theorem, show that (i) (x-2) is a factor of x^(3)-2x^(2)-9x+18 . Hence factorise the expression x^2-2x^2-9x+18 completely. (ii) (x+5) is a factor of 2x^3+5x^2-28x-15 . Hence factorise the expression 2x^3+5x^2-28x-15 completely. (iii) (3x+2) is a factor of 3x^(3)+2x^(2)-3x-2 . Hence factorise the expression 3x^3+2x^2-3x-2 completely.

Use factor theorem to show that x^(4)+2x^(3)-2x^(2)+2x-3 is exactly divisible by (x+3) .

Find the quotient and remainder when 6 x^(4) + 11x^(3) + 13x^(2) - 3x + 27 is divided by 3x + 4. Also check the remainder obtained by using remainder theorem.

Using remainder theorem, find the remainder when x^(4)+x^(3)-2x^(2)+x+1 is divided by x-1 .

Devide x^(3)+4x^(2)-3x-10 by x+1 and verify your remainder by remainder theorem.

Divide the first polynomial by the second polynomial and find the remainder using remainder theorem. (2x^3-2x^2+ax-a),(x-a)