Faster way of determining the coefficient of a polynomial function? Question: Determine if the leading coefficient of the function "a", is positive or negative. 
a) $$f(x)=(x-3)^2(x+1)(x+2)^3$$
In my notes I stated the sign of the leading coefficient without work but in order to get the answer now I had to expand the polynomial function out. Any help would be appreciated.
-Jack

In general once we know the roots of a polynomial function in the form
$$f(x)=k(x-x_1)(x-x_2)...(x-x_n)$$
we can easily find all the coefficient for 
$$f(x)=a_nx^2+a_{n-1}x^{n-1}+...+a_1x+a_0$$
indeed
$$a_n=k$$
$$a_{n-1}=-(x_1+x_2+...+x_n)$$
$$a_{n-2}=x_1x_2+x_1x_3...+x_{n-1}x_n$$
$$...$$
$$a_0=(-1)^{n}\prod x_i$$
Take also a look here Relation betwen coefficients and roots of a polynomial
