Question

Which is a factor of x2- 14x + 48?

Answer 1

look at the last number 48. It is +, that means both factors will have the same sign
look at the"middle" number -14. It is -, so the biggest factor is negative.
based on the same sign rule, both factors are negative

now list the pairs of numbers that when multiplied together give 48
1,48
2,24
3,16
4,12
6,8

look for a pair, where if both are negative, add to -14. those will be the numbers a and b you use in
(x+ a) (x+b)

Answer 2

Do it like...
x^2 -8x-6x +48
= x(x-8) -6(x-8)
Taking x-8 common ,
= (x-8)(x-6)
So the two factors are 8 and 6, so the possible values of x are 6 and 8.