[tex] x^{2} - 5x + 4 [/tex]
in order to factor this trinomial, we look for two numbers that multiply to [tex] 4 [/tex] and add up to [tex]negative~5[/tex]
pairs of numbers that multiply to [tex] 4 [/tex] include
[tex] 1,~4 [/tex]
and
[tex] 2,~2 [/tex]
only the pair of [tex]negative~1[/tex] and [tex]negative~4[/tex] add up to [tex]negative~5[/tex] so we use that pair.
with this we should get
[tex] (x - 1)(x - 4) [/tex]
which means that the two binomials that could potentially be you answer are
[tex] x - 1 [/tex]
and
[tex] x - 4 [/tex]
