Step 1

We have to factor the polynomial:

\(m^{2}-5m-14\)

Factorizing by middle term splitting method,

Here,

\(14=7\times 2\)

and middle term can be replaced as:

\(-7+2=-5\)

Therefore,

\(m^{2}-5m-14=m^{2}-7m+2m-14=mm-7+2m-7\)

Step 2

Taking common \(m-7\), we get

\(mm-7+2m-7=m-7m+2\)

Hence, factor of the polynomial is \(m-7m+2\).

Here greatest factor is \(m+2\) since m is increased by 2 but in \(m-7\), m is decreased by 7.