`(x+1)(x+2)(x+6)=x^(3)+9x^(2)+4(7x-1)`

Verify the division algorithm for the polynomials p(x)=2x^(4)-6x^(3)+2x^(2)-x+2andg(x)=x+2 . p(x)=2x^(3)-7x^(2)+9x-13,g(x)=x-3 .

Check whether the following are quadratic equations : (1) (x-3)^(2)=x(2x-5) (2) (2x-3)(8x+1) = (4x+5)(4x-5) (3) (5x+3)(x-2)=(4x+3)(2x-1) (4) (2x+5)^(3)=8(x-1)^(3) (5) x^(2)+7x-8=x(x+5) (6) x^(3)+9x^(2)-7x+2=(x+3)^(3)

lim_(x rarr oo) (3x^(3) + 2x^(2) - 7x + 9)/(4x^(3) + 9x -2)

a (x) = 3x ^ (6) + 7x ^ (4) + 9x ^ (2) + 2x + 1, b (x) = 2x + 2

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

Simplify the following : 5x^(4) - 7x^(2) +8x - 1 +3x^(2) - 9x^(2) + 7 - 3x^(4)+11x - 2 +8x^(2)

Evaluate lim_(x to sqrt(3)) (3x^(8) + x^(7) - 11x^(6) - 2x^(5) 9x^(4) - x^(3) + 35x^(2) + 6x + 30)/(x^(5) - 2x^(4) + 4x^(2) - 9x + 6)