Answer
not factorable with integer coefficients
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the quadratic expression $x^2+bx+c,$ find two numbers, $m_1$ and $m_2,$ whose product is $c$ and whose sum is $b$. Then, express the factored form as $(x+m_1)(x+m_2).$
$\bf{\text{Solution Details:}}$
In the given expression, $
m^2-11m+60
,$ the value of $c$ is $
60
$ and the value of $b$ is $
-11
.$
The possible pairs of integers whose product is $c$ are
\begin{array}{l}\require{cancel}
\{1,60\}, \{2,30\}, \{3,20\}, \{4,15\}, \{5,12\}, \{6,10\},
\{-1,-60\}, \{-2,-30\}, \{-3,-20\}, \{-4,-15\}, \{-5,-12\}, \{-6,-10\}
.\end{array}
Among these pairs, none gives a sum of $b.$ Hence, the given expression is $\text{
not factorable with integer coefficients
.}$