For the given trinomial
[tex]a=-1, b=1 ,c=42[/tex]
We need to multiply a by c
[tex] -1 \times 42 = - 42[/tex]
We split the middle term with these two factors
[tex]
7,-6[/tex]
To obtain,
[tex] - {x}^{2} + 7x -6x + 42[/tex]
We now factor
[tex] - {x}^{2} + x + 42 \: = x( - x + 7) + 6( - x + 7)[/tex]
This implies
[tex] - {x}^{2} + x + 42: = (x + 6)(7 - x)[/tex]
