Find all integers b such that the trinomial $x^2+bx+10$ can be factored.

A) $\pm 7,\pm 11$
B) 10,1
C) $\pm 2,\pm 5$
D) -2,-5
E) -7,-11

For a trinomial $x^2+bx+10$ to be factored, the factors of the constant term (10) must add up to the middle coefficient $b$ . The factors of 10 are 1 and 10, or 2 and 5, which can be either positive or negative. Adding these factors gives possible $b$ values of $\pm 11$ (from $\pm 1$ and $\pm 10$ ) and $\pm 7$ (from $\pm 2$ and $\pm 5$ ).