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

You asked for the leading coefficient of $$f(x)=(x-3)^2(x+1)(x+2)^3$$
As you see this is a polynomial of degree $6$ therefore you want to know the coefficient of $x^6$
How many $x^6$ are there in the product?
Well there is only $1$ because you need to multiply the leading coefficients of each factor to get the leading coefficient of the product.  
In our case all the leading coefficients of factors are $1$ so the leading coefficient of the product is also $1$  
