`P(x)=x^3 + ax^2 - x+ b` and
Find the relation between a and b for x-1 to be a factor of P(x).

Find the value of k if x-1 is the factor of P(x)=2x^(2)+kx+sqrt(2)

Find the value of a if (x - 5) is a factor of (x^(3)-3x^(2)+ax-10)

Find the value of k if x-1 is the factor of P(x) =kx^(2)-sqrt(2)x+1

Find the relationship between a and b so that the function f defind by f(x)= {(ax+1, if x le 3),(bx+3, if x gt 3):} is continuous at x=3

Find the relationship between a and b so that the function defined by f(x) = {(ax+1,if, x le 3),(bx+3,if, x gt 3):} is continuous at x = 3.

Find the Factor Theorem, x +2 is a factor of x ^(3) + 2x ^(2) + 3x + 6.

If x = alpha,beta satisfy both the equations cos^(2)x + acosx + b = 0 and sin^(2)x + p""sinx + q = 0 , then the relation between a, b, p and q is :

(i) Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following: p(x)=x^3-3x^2+5x-3,g(x)=x^2-2 (ii) Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following: p(x)=x^4-3x^2+4x+5,g(x)=x^2+1-x (iii) Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following: p(x)=x^4-5x+6,g(x)=2-x^2

If x^2+p x+1 is a factor of the expression a x^3+b x+c , then