Which first degree polynomial is added to the polynomial `5x^3+3x^2` to get `x^2-1` as a factor.

What number should be added to the polynomial x^3-2 x^2+x-4 to get (x-2) as a factor of the polynomial?

Which number added to the polynomial 3x^2-4x-1 gives a polynomial with (x-1) as a factor.

What is the smallest natural number k for which the polynomial 2 x^2+k x+6 can be written as a product of two first degree polynomials? Write down the polynomial using 'k' and express it as the product of two first degree polynomials.

What number should be added to the polynomial p(x)=x^2+x-1 , so that '(x-2)' is a factor of the new polynomial?

Show that the polynomial x^2+ x + 1 has no first degree factors..

If x-1 is a factor of the polynomial 5x^3-4x^2+x-k ,what number is k?

Consider the polynomial p(x)= x^2-5x+6 :- Is (2x-1)a factor of p(x)? Why?

Check whether (x-3) is a factor of the polynomial 2 x^3-x^2-3 x+4

Consider the polynomial P(x)=ax^3-x^2-bx-1 .Find P(1) .