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

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?

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

In the polynomial x^2+k x+6 , what number must be taken as 'k' to get a polynomial for which 'x-1' is a factor? Find also the other factor of that polynomial.

In the polynomial kx^2+2 x-5 , 'what number must be taken as 'k', to get a polynomial for which 'x-1' is a factor?

If x^2+x+2=(x-2)(x+a)+b a) Find 'a' and 'b'. b) What number should be added to x^2+x+2 to get a polynomial having a factor '(x+3)'

Consider the polynomial P(x)=ax^3-x^2-bx-1 Will, P(x) have both (x+1) and (x-1) as factors for any numbers a and b? Justify.

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

In each pair of polynomials given below, find the number to be subtracted from the first to get a polynomial for which the second is as factor. Find also the second factor of the polynomial got on subtracting the number:- x^2-4x-3,x-1 .