# Isomorphic polynomial rings

## Homework Statement

I am required to prove that $$F_5[x]/(x^2 + 2) isomorphic to F_5[x]/(x^2 + 3)$$

now I have the solution in front of me so I more or less know what's going on, however there are some points of confusion......

....the solution states that $$x \rightarrow 2x$$ will define the desired isomorphism. The next line asserts that

$$x^2 \rightarrow (2x)^2 + 2, 4x^2 + 2= -(x^2 -2) = -(x^2 +3)$$

$$x^2 = -2=3$$ ............?????

..what is going on here surely $$x^2 \rightarrow 4x^2$$