help with polynomials..."from 19x^2+11x+5 subtract -5x^2-6x-6"?

combine like terms!

19x^2 + 11x + 5
-
-5x^2 - 6x - 6
----------------------
24x^2 + 17x + 11

24x² + 17x + 11

1. -5x^2-6x-6 - (19x^2+11x+5)
= -24x^2 -17x -11

2. -12x^2-19x+8 - ( -15x+17x-18)
= -12x^2-19x+8 +15x -17x+18
= -12x^2 -36x + 26

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1. 19x^2 + 11x + 5 - (-5x^2-6x-6)
Get rid of parenthesis

=19x^2 + 11x + 5 + 5x^2 + 6x + 6

Combine like-terms.
=24x^2 +17x +11

2. -12x^2-19x+8 -( -15x+17x-18)

Get rid of parenthesis
= -12x^2 -19x + 8 +15x -17x +18

Combine like-terms
= -12x^2 - 36x + 26

1. 19x^2 + 11x + 5 - (-5x^2-6x-6)
applying distributive property and combining like terms

=19x^2 + 11x + 5 + 5x^2 + 6x + 6
=24x^2 +17x +11

2. -12x^2-19x+8 -( -15x+17x-18)
=-12x^2-19x+8 +15x -17x+18
=-12x^2 -36x + 26

To subtract that second polynomial from the first one, just match up terms with the same degree (19x^2, -5x^2) and do the subtraction with their coefficients. (5x^2+3x-2) - (1x^2+2x+3) = 4x^2+x-5

The how much greater question is ambiguous. It depends on what x is. If x is 0, then the first one is greater... if x is -10000000, then the second is (probably... i didn't actually calculate it) greater.

(19x^2+11x+5) - (-5x^2-6x-6)

which can be written as follows

19x^2 + 11x + 5 + 5x^2 + 6x +6

The -5x^2-6x-6 is all positive because you're multiplying by negative and negative times negative is positive.
Now you can only add/subtract coefficients with similar power meaning coefficient of x^2 can only be added/subbtracted with another coefficient with x^2 term. So if you group above equation with similar coefficient it will look like following.

= (19x^2 + 5x^2) + (11x + 6x) + (5 + 6)
= (19+5) x^2 + (11+6) x + (5+6)
= 24 x^2 + 17x + 11

To answer your second question, you need to divide first the polynomial by the second polynomial. The answer will be some polynomial. There are several ways to divide polynomials. One of them is to use long division. First you need to factor both polynomials and cancel out similar terms and then use long division to divide rest. Here's the site that explains it in detail or just google long division for more info.
http://campus.northpark.edu/math/PreCalculus/Algebraic/Polynomial/Factoring/index.html
http://en.wikipedia.org/wiki/Polynomial_long_division