Show that `(3x+7)^2-84x`=`(3x-7)^2

Show that (x +4) ,(x-3) and (x-7) are factors of x ^(3) - 6x ^(2) - 19 x + 84.

Show that (x-2) , (x+3) and (x-4) are factors of x ^(3) -3x ^(2) -10x + 24.

Without actual division, show that f(x) = 2x^(4) - 6x^(3) + 3x^(2) + 3x - 2 is exactly divisible by x^(2)- 3x + 2 .

Solve the inequality (x+3)(3x-2)^5(7-x)^3(5x+8)^2 >= 0.

Show that the lines (x-5)/7=(y+2)/(-5)=z/1 " and " x/1=y/2=x/3 are perpendicular to each other.

Show that : tan 3x tan 2x tan x =tan 3x-tan2x-tanx

Show that tan 3x tan 2x tan x = tan 3x - tan 2x - tan x

One of the positive roots of the equtions (2x- 7) ( 3x-5) =0

Show that the lines (x-5)/7=(y+2)/(-5)=z/1" and "x/1=y/2=z/3 are perpendicular to each other.

lim _ ( xto infty ) ( 3x^(2) -4x + 5)/( 7x^(2) + 2x +3)