If `2x+4=A(2x+3)+B` , find A and B

Let A and B are two sets such that n (A) = 3 and n (B) = 2. If (x,1), (y,2),(z,1) are in A xx B , find A and B, where x,y and z are distinct elements.

Consider the polynomial p(x)=x^3+a x^2-x+b a) Find the relation bétween 'a' and 'b' if (x-1) is a factor of p(x) b) What is the relation between 'a' and 'b' if (x-2) is a factor of p(x) ? c) Find a and 'b' so that both (x-1) and (x-2) are factors of p(x).

If x^2+x+2=(x-2)(x+a)+b a) Find 'a' and 'b'. b) What number should be added to x^2+x+2 to get a polynomial having a factor '(x+3)'

If A=[[1 ,-2 , 3],[ -4, 2 ,5]] and B=[[2 , 3],[ 4, 5], [2 , 1]] , then find A B, B A . Show that AB ne BA .

If f(x) = (ax^2 +b)^3 , then find the function g such that f(g(x)) = g (f(x)) .

(a)If A={x in R:x^2-5x+6=0} and B={x in R:x^2=9} , find AxxB .

If the curve y = ax^(2) - 6x + b passes through (0, 2) and has its tangent parallel to the x-axis at x = (3)/(2) , then find the values of a and b.

If A= [(2,-1),(3,1)] and B = [(1,4),(7,2)] ,find 3A - 2B.

If A=[[8 ,0], [ 4 , -2],[ 3 , 6]] and B=[[2 , -2], [ 4 ,2], [ -5 , 1]] , then find the matrix X , such that 2 A+3 X=5 B .