Let f(x) = n^2 - 1, where n is an integer and n > = 1. is f(x) always divisible
by (x - 1)? justify.

Yes.

Step-by-step explanation:

(Assume x is not 1.)

is always divisible for integers greater than 1.

Let's use synthetic division:

1  |   1x^n     + 0x^(n-1)    +0x^(n-2) + ....+0x^3+0x^2+0x -1

  |                  1                 1                      1         1        1     1

---------------------------------------------------------------------------------

      1              1                 1                      1         1         1      0

We see the remainder is 0 which means that divides .

The quotient is .

the answer is y < -3 or   y > 3

-3y > 7 + 2

-3 y > 9

y < -3