If `p x^4+q x^3+r x^2+s x+t`=`|[x^2+3x, x-1, x+3],[x+1, 2-x, x-3], [x-3, x+4, 3x]|` then

If |{:(x,-6,-1),(2,-3x,x-3),(-3,2x,x+2):}|=0 then x = ……..

The value of p(x) = x^(3) + x^(2) - 3x-3 at x = -1 is …… .

x^(3) + 3x^(2) + 3x + 2 = (x+2) (………)

The total number of distinct x in R for which |[x, x^2, 1+x^3] , [2x,4x^2,1+8x^3] , [3x, 9x^2,1+27x^3]|=10 is (A) 0 (B) 1 (C) 2 (D) 3

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) - 20x + 12, g (x) = 3x -2 (v) f (x) = 4x ^(3) + 20 x ^(2) + 33 x +18, g (x) =2x +3

If |{:(x+1,x-1),(x-3,x+2):}|=|{:(4,-1),(1,3):}| then find x

Determine which of the following polynomials has (x +1) as a factor. (i) x ^(3) -x ^(2) -x +1 (ii) x ^(4) - x ^(3) + x ^(2) -x +1 (iii) x ^(4) + 2x ^(3) + 2x ^(2) + x +1 (iv) x ^(3) -x ^(2) - (3- sqrt3) x + sqrt3

Divide p(x) by g(x), where p(x) = x+3x^(2) -1 and g(x) = 1+x .