I am trying to find a polygon that its graph take this four points as extra point. 
I tried
f := x -> a*x^7 + b*x^6 + c*x^5 + d*x^4 + k*x^3 + l*x^2 + m*x + n;
solve([f(-2) = -5, f(5) = -6, f(6) = 1, f(-1) = 2, eval(diff(f(x), x), x = -2) = 0, eval(diff(f(x), x), x = 5) = 0, eval(diff(f(x), x), x = 6) = 0, eval(diff(f(x), x), x = -1) = 0], [a, b, c, d, k, l, m, n]);

I get. Is there a polymial with lower degree take this four point as extra points?

When I input
restart;
a := 2;
b := 3;
p := x^2 - a*x - b*x +a*b ;
I get p := x^2 - 5*x + 6
How can I get x^2 - 2 x - 3x + 6.
General question. I have (a,b) in a list [[2,3],[-3,7],[9,10]]. How to subtitute them to get the result
[[x^2 - 2x - 3x + 6, x^2 + 3x - 7x -21, x^2 - 9x - 10x + 90]? 

I am trying to draw this pictures in LaTeX, then I need to find their parametric equations. How can I get them?
 

I want to construct a quadrilateral ABCD with A = 120 degrees, B = 80 degrees, C = 110degrees. I do know how to start. How do I construct one option of a quadrilateral with measure of its four angles?

I am trying to solve the equation: 
solve(cos(3*x - Pi/12) = cos(2*x + Pi/7), x, allsolutions).
It is difficult for me to get the resullt. 
Solve by my hand. I tried
restart;
a := 3*x - Pi/12;
b := 2*x + Pi/7;
S1 := solve(a = 2*Pi*k + b, x);
S2 := solve(a = 2*Pi*k - b, x);
S := ((S1 union S2) assuming k::integer);
I get the answer

Can I get the result by command 
solve(cos(3*x - Pi/12) = cos(2*x + Pi/7), x, allsolutions).