`|(x+4, 2x, 2x),(2x, x +4, 2x),(2x, 2x ,x+4)| = (5x + 4)(4 - x)^(2)`.

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

int(x^3 + 5x^2 - 4)/(x^2) dx .

f(x) = {((sin 2x)^(tan^(2)2x), x ne pi/4),(k, x = pi/4):} . If f(x) is continuous at x = pi/4 , then k =

Find |A| If A = [(x^2, 2x), (x^4 , 5x)]

Find the value of x if, |(2,4),(5,1)| = |(2x, 4),(6, x)|

cos 4x=cos 2x

If the determinant |(cos2x, sin^2x,cos4x),(sin^2x , cos2x,cos^2x),(cos4x,cos^2x,cos2x)| is expanded in powers of sinx , then the constant term in the expansion is :

Prove that (cos 4 x + cos 3 x + cos 2x)/(sin 2x + sin 3 x + sin 4 x ) = cot 2 x .

Find the values of a and b for which zeros of q(x) = x^(3) + 2x^(2) +a are also the zero of p(x) = x^(5) - x^(4) - 4x^(3) + 3x^(2) + 3x +bp . Also, find zeros of p(x) which are not zeros of q(x) .