Verify the division algorithm for the polynomials `p(x)=2x^(4)-6x^(3)+2x^(2)-x+2andg(x)=x+2`. `p(x)=2x^(3)-7x^(2)+9x-13,g(x)=x-3`.

Verify division algorithm for the polynomials f(x)=8+20x+x^(2)-6x^(3) and g(x)=2+5x-3x^(2)

Verify division algorithm for the polynomials p(x)=3x^(4)-4x^(3)-3x-1andg(x)=x-2 . Find p(2) . What do you observe ?

Verify division algorithm for the polynomials p(x)=x^(3)+x^(2)+2x+3andg(x)=x+2 . Find p(-2) . What do you observe ?

The product of uncommon real roots of the p polynomials p(x)=x^(4)+2x^(3)-8x^(2)-6x+15 and q(x)=x^(3)+4x^(2)-x-10 is :

Find the quotient and remainder in each of the following and verify the division algorithm : (i) p(x) =x^(3)-4x^(2)+2x-1 is divided by g(x)=x+2. (ii) p(x) =x^(4)+2x^(2)-x+1 is divided by g(x) =x^(2)+1 . (iii) p(x) =2x^(4)-3x^(3)+x^(2)+5x-3 is divided by g(x) =x^(2)+x-1 . (iv) p(x) =x^(4)-5x^(2)+6 is divided by g(x)=x+2.

Check whether g(x) is a factor of p(x) by dividing the first polynomial by the second polynomial: (i) p(x) = 4x^(3) + 8x + 8x^(2) +7, g(x) =2x^(2) -x+1 , (ii) p(x) =x^(4) - 5x -2, g(x) =2-x^(2) , (iii) p(x) = 13x^(3) -19x^(2) + 12x +14, g(x) =2-2x +x^(2)

Divide P(x)=2x^4+3x^3-2x^2-9x-12 by g(x)=x^2-3

Using Division Algorithm prove that the polynomial g(x) = x^(2) + 3x + 1 is a factor of f(x) = 3 x^(4) + 5 x^(3) - 7 x^(2) + 2x + 2

Apply the division algorithm to find the quotient and remainder on dividing p (x) by g (x) as given below : p(x)=x^3-3x^2+5x-3, g(x)= x^2-2 .