[" 5.Verify division algoristim "],[" for the polynomial "],[qquad [p(x)=3x^(4)-4x^(3)-3x-1],[" ind "g(x)=(x-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 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 .

Find the remainder when the polynomial p(x)=x^(3)-3x^(2)+4x+50 is divided by g(x)=x+3 .

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

For what value of a is the polynomial p(x)=2x^(4)-ax^(3)+4x^(2)+2x+1 is divisible by 1-2x

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.

If the polynomial p(x)=x^(3)+6x^(2)+4x+k is divisible by (x + 2), then k =

Verify that 2 is a zero of the polynomial x^(3)+4x^(2)-3x-18.