Find the factors of the expression: $(40 + 3\mathrm{x} - {\mathrm{x}}^2)$ 

Given expression: $(40 + 3\mathrm{x} - {\mathrm{x}}^2)$.

The expression can be rewritten as: $- ({\mathrm{x}}^2 - 3\mathrm{x} - 40)$

Now, applying the middle-term split, we get: 

$=- ({\mathrm{x}}^2 - 3\mathrm{x} - 40)$

$\begin{array}{l}= - ({\mathrm{x}}^2- 8\mathrm{x} +5\mathrm{x} - 40)\\ \\ = -\{\mathrm{x}\left(\mathrm{x} - 8\right) + 5\left(\mathrm{x} - 8\right)\}\\ \\ = -\left\{\right(\mathrm{x} - 8\left)\right(\mathrm{x} + 5\left)\right\}\\ \\ =\mathbf{(}\mathbf{5}\mathbf{ }\mathbf{+}\mathbf{ }\mathbf{x}\mathbf{)}\mathbf{(}\mathbf{8}\mathbf{ }\mathbf{-}\mathbf{ }\mathbf{x}\mathbf{)}\end{array}$ .

Hence, the factors of  $(40 + 3\mathrm{x} - {\mathrm{x}}^2) =\mathbf{ }\left(5 + x\right)\left(8 - x\right)$  .