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

Check whether '(x+2)' and '(x-5)' are factors of the polynomial x^2+7 x+10

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

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

Check whether x - 1 is a factor of 3x^3-2x^2-3x+2 .

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

The value of x for which the polynomial 2x ^(3) - 9x ^(2) + 12 x + 4 is a decreasing function of x, is :

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?

Prove that none of the polynomials below can be factored into a product of first degree polynomials:- x^2-x+1 .

p(x) = (4x^2 - 1)(x + 2) . Write p(x) as the product of first degree factors. Write p(x) in the form of a third degree polynomial. What is the remainder obtained by dividing 4x^3 + 6x^2- x + 2 by (x + 2). What is the remainder obtained by dividing 4x^3+6x^2-x+1 by (2x-1).