Which student factored the expression x3 - 7x - x2 + 7 correctly based on their answer below?

jane: (x + 1)(x2 - 7)
mariah: (x - 1)(x2 + 7)
roger: (x + 1)(x2 + 7)
nethan: (x - 1)(x2 - 7)

jane
mariah
roger
nethan

We can check the end terms first

for
(a+b)(c+d), the first term of the expanded is ac and the last term is bd

so
the expanded is x^3 and last is +7

jane will have a lst term of -7 so no
mariah wil have last term of -7 as well, so no
only rojer and nethan have last tem of +7

so we can do the rest of it by doing the OL part of FOIL

do either roger or nethan
let's do nethan

F=x^3
O=-7x
I=-x^2
L=7
yep

it is nethan