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, and the sum of the roots is 
. So we need to find a combination of integers that multiply to and add up to . Let's call the roots of the equation p, q, and r. From Vieta's, we get that 
and 
. Looking at the factors of , which is 
, we try to split the numbers in a way that gives us the correct sum and product. Trying 3, -2, and -8, we see that they add up to 
and multiply to 
, so they work. That means the roots of the polynomial are -3, -2, and -8, and the factorization is 
. Multiplying it out, we get 
, so we find that a = 46.
+1 w
![\[\iint_{R} \sin(xy) \,dx\,dy, \quad R = \left[0, \frac{\pi}{2}\right] \times \left[0, \frac{\pi}{2}\right]\]](http://latex.artofproblemsolving.com/a/2/0/a205868dd99f4794de53ad1db50f34b17c70a923.png)
be a group, 
a subgroup of 
and 
an endomorphism with the following property:
such that for any 
there exist 
with 
and 
, for any 
.
is abelian.
is a subgroup of , prove that 
are complex numbers with absolute value 
. For 
define 
. Given that the sequence 
converges. Show that,
.
such that there exists an integer polynomial 
with no integer roots and a constant 
such that
has at least 
distinct prime divisors for all positive integers 
.
is an integer, then there exist invertible matrices 
with non-zero entries such that:![\[A_1^{-1} + A_2^{-1} + \ldots + A_n^{-1} = (A_1 + A_2 + \ldots + A_n)^{-1}.\]](http://latex.artofproblemsolving.com/a/f/9/af9ff29771952abe37a00f3830c72e8c517e1cd6.png)
be a closed and countable set. Prove that if the analytic function 
is bounded, then 
is constant.
be an integer with 
Over all real polynomials 
of degree 
what is the largest possible number of negative coefficients of 
fibonacci numbers (
) find all n such that:
and 
topic in College Math :coolspeak:
