[" (i) "t^(2)-3,20],[" (ii) "x^(2)+3x+1,3x^(4)+5x^(3)-7x^(2)+2x+2],[" (t) "-5^(5)-4x^(3)+x^(2)+3x+1]

Check whether the first polynomial is factor of Second polynomial by dividing: t^2-3,2t^(4)+3t^(3)-2t^(2)-9t-12 (ii) x^(2)+3x+1,3x^(4)+5x^(3)-7x^(2)+2x+2 (iii) x^(3)-3x+1,x^(5)-4x^(3)+x^(2)+3x+1

If A, B, C are the remainders of x^(3) - 3x^(2) - x + 5, 3x^(4) - x^(3) + 2x^(2) - 2x - 4, 2x^(5) - 3x^(4) + 5x^(3) - 7x^(2) + 3x - 4 when divided by x + 1, x + 2, x - 2 respectively then the ascending order of A, B ,C is

From the sum of 6x^(4) - 3x^(3) + 7x^(2) - 5x + 1 and -3x^(4) + 5x^(3) - 9x^(2) + 7x - 2 subtract 2x^(4) - 5x^(3) + 2x^(2) - 6x - 8

Subtract : 2x^(4) - 7x^(2) + 5x + 3 " from " x^(4) - 3x^(3) - 2x^(2) + 3

If f(x) = 2x^(4) + 5x^(3) -7x^(2) - 4x + 3 then f(x -1) =

Divide 2x^5 -3x^4 +5x^3 -7x^2 +3x -4 by x-2.

Divide 2x^5 -3x^4 +5x^3 -7x^2 +3x -4 by x-2.

Subtract: 7x^(4)-5x^(3)+4x^(2)+3x-3 from 6x^(4)-4x^(3)-8x^(2)-2x+7

Find the quotient and remainder of the following using synthetic division: (i) (x^(3) +x^(2) -7x-3) +(x-3) (ii) (x^(3) +2x^(2) -x-4) +(x+2) (iii) (3x^(3) -2x^(2) +7x -5) +(x+3) (iv) (8x^(4) -2x^(2) +6x +5) +(4x+1)

Evaluate: (i) int(5x^(2) + 2x^(-5) - 7x + 1/(sqrt(x)) +5/x) dx (ii) int(3sinx - 4 cosx + 5 sec^(2) x - 2cosec^(2)x) dx (iii) int(1-x)(2+3x)(5-4x)dx (iv) int((3x^(4) - 5x^(3) + 4x^(2) -x + 2)/(x^(3)))dx , (v) int(x^(2) + 1/(x^(2)))^(3) dx