Answer
$-(t+4)(t-11)$
Work Step by Step
We start by factoring out -1. We have $-t^2+7t+44=-(t^2-7t-44)$
The factor pairs of -44 are
1 and -44, -1 and 44
2 and -22, -2 and 22
4 and -11, -4 and 11
4 and -11 add up to -7
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