# Thread: a+1 is not a factor of a^2+1

1. ## a+1 is not a factor of a^2+1

$a+1$ is not a factor of $a^2+1$.

However, when $a=-3$, we get -2 is not a factor of 10, which is false. Could someone explain this anomaly?

2. ## Re: a+1 is not a factor of a^2+1

the polynomial in a, a+1, is not a factor of the polynomial in a, a^2 + 1.

this does not mean that for some particular NUMBER a, a+1 is not a factor of a^2 + 1, which is clearly false: for example a = 1 gives 2 divides 2, which is true.

there is a difference between the function defined by f(a) = a+1, and the value f(a) for some particular a.

two unequal functions can nevertheless have intersecting graphs.

3. ## Re: a+1 is not a factor of a^2+1

Because it's not true for all the values you'll give to a, take for example a=5 then a+1=6 which is not a factor of a^2+1=26. If you take for example a^2-1, then a-1 is a factor, so for every value of a it will still be a factor.