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 ?

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

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

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

In each of the following cases, use factor theorem to find whether g(x) is a factor of the polynomial p(x) or not. p(x)= x^(3)-3x^(2)+6x-20 g(x)= x-2

Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing f(x)=x^3-6x^2+11 x-6 by g(x)=x^2+x+1

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