Let f(x) = n^2 - 1, where n is an integer and n >= 1. Is f(x) always divisible
1 answer:
Answer:
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
.
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