10.3. Find all quadratic trinomials $P(x)=x^{2}+b x+c$ such that $P(x)$ has integer roots, and the sum of its coefficients (i.e., $1+b+c$) is 10.
Answer. $(x-2)(x-11),(x-3)(x-6), x(x+9),(x+4)(x+1)$. Solution. See problem 9.3.