`" If " |{:(x^(2)+x,,x+1,,x-2),(2x^(2)+3x-1,,3x,,3x-3),(x^(2)+2x+3,,2x-1,,2x-1):}|=xA +B` then find A and B

Without expanding a determinant at any stage, show that abs((x^2+x ,x+1 , x-2),(2x^2+3x-1 ,3x , 3x-3) , (x^2+2x+3, 2x-1 ,2x-1))=xA+B ,where A and B are determinant of order 3 not involving xdot

If |(x^2+x,x+1,x-2),(2x^2+3x-1,3x,3x-3),(x^2+2x+3,2x-1,2x-1)|=ax-12 then 'a' is equal to (1) 12 (2) 24 (3) -12 (4) -24

If |(x^2+x,x+1,x-2),(2x^2+3x-1,3x,3x-3),(x^2+2x+3,2x-1,2x-1)|=ax-12 then 'a' is equal to (1) 12 (2) 24 (3) -12 (4) -24

lim_(xrarr1) [(x-2)/(x^(2)-x)-(1)/(x^(3)-3x^(2)+2x)]

If f(x) = |(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(x-1),x(x-1)(x-2),x(x+1)(x-1))| , using properties of determinant, find f(2x) - f(x).

If a,b,c are in A.P.and f(x)= |(x+a,x^2+1,1),(x+b, 2x^2-1,1),(x+c,3x^2-2 , 1)| , then f'(x) is :

If (3x+4)/(x^(2)-3x+2)=A/(x-2)-B/(x-1) then (A, B) =

Evaluate: lim_(xrarr1) [(x-2)/(x^(2)-x)-(1)/(x^(3)-3x^(2)+2x)]

Simplify: (x^3-2x^2+3x-4)(x-1)-\ (2x-3)(x^2-x+1)

If f(x)=|[x-2, (x-1)^2, x^3] , [(x-1), x^2, (x+1)^3] , [x,(x+1)^2, (x+2)^3]| then coefficient of x in f(x) is