[" 11.Verify division algorithm for the polynomials "f(x)=8+20x+x^(2)-6x^(3)],[" and "g(x)=2+5x-3x^(2)]

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 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 ?

By applying division algorithm prove that the polynomial g(x)=x^(2)+3x+1 is a factor of the polynomial f(x)=3x^(4)+5x^(3)-7x^(2)+2x+2

By applying division algorithm prove that the polynomial g(x)=x^(2)+3x+1 is a factor of the polynomial f(x)=3x^(4)+5x^(3)-7x^(2)+2x+2

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 f(x)=x^(4)-5x+6 by g(x)=2-x^(2)

By applying division algorithm prove that the polynomial g(x)=x^2+3x+1 is a factor of the polynomial f(x)=3x^4+5x^3-7x^2+2x+2.

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.

Apply the division algorithm to find the quotient and remainder on dividing f(x)=x^4-5x+6 by g(x)=2-x^2