Show that ( x- 3) is a factor of `x^(3) + 9x^(2) -x - 105`

Show that (x-5) is a factor of x^(3)-3x^(2)-4x-30 .

Show that (2x-3) is a factor of (x+2x^(3)-9x^(2)+12) .

Show that, x -2 is a factor of x ^(3) - 2x ^(2) + 3x - 6.

Show that: 2x-3 is a factor of x+2x^3-9x^2+12

Show that (x-3) is a factor of: 2x^3+7x^2-24x-45 .

Using the Factor theorem, show that (i) (x-2) is a factor of x^(3)-2x^(2)-9x+18 . Hence factorise the expression x^2-2x^2-9x+18 completely. (ii) (x+5) is a factor of 2x^3+5x^2-28x-15 . Hence factorise the expression 2x^3+5x^2-28x-15 completely. (iii) (3x+2) is a factor of 3x^(3)+2x^(2)-3x-2 . Hence factorise the expression 3x^3+2x^2-3x-2 completely.

Show that (x+2) is a factor of f(x) = x^(3) + 5=4x^(2) + x - 6.

By actual division show that x+2 is a factor of x^(3)+4x^(2)+3x-2 .

If a is a rational number such that (x-a) is a factor of x^(3)-3x^(2)-3x +9 , then

Show that (x-3) is a factor of the polynomial x^(3)+x^(2)-17x+15 .