The G.C.D of `x^(4) + 3x^(3) + 5x^(2) + 26x + 56` and `x^(4) + 2x^(3) - 4x^(2) - x + 28` is `x^(2) + 5x + 7` Find their L.C.M.

Find the L.C.M of x^(3) + x^(2) - x - 1 and x^(3) + 3x^(2) - x - 3

Let P(x) = 4x^(2) - 3x + 2x^(3) + 5 and q(x) = x^(2) + 2x + 4 find p ( x) - q(x) .

Use the Factor Theorem to determine whether g (x) is factor of f(x) in each of the following cases: (i) f (x) = 5x ^(3) + x ^(2)-5x -1, g (x)=x +1 (ii) f (x) = x ^(3) + 3x ^(2) + 3x +1 , g(x) =x +1 (iii) f (x) =x ^(3) - 4x ^(2) +x + 6, g (x) =x -2 (iv) f (x) = 3x ^(3) + x^(2) - 20x + 12, g (x) = 3x -2 (v) f (x) = 4x ^(3) + 20 x ^(2) + 33 x +18, g (x) =2x +3

Find the square root of (6x^(2) + 5x - 6) (6x^(2) - x - 2) (4x^(2) + 8x + 3)

Find the GCD of the given polynomials 3x^(4)+6x^(3)-12x^(2)-24x, 4x^(4)+14x^(3)+8x^(2)-8x

If f'(x) = 3x^2 - 4x + 5 and f(1) = 3 then find f(x).