# Math Help - algebraic numbers

1. ## algebraic numbers

x is algebraic and let y = x + 3. Is y algebraic? and why is it?

2. ## Re: algebraic numbers

Originally Posted by thomasboateng
x is algebraic and let y = x + 3. Is y algebraic? and why is it?
Let f(x) be the irreducible polynomial for x over F. Then, the irreducible polynomial for y over F is f(y-3). So, y is algebraic.

3. ## Re: algebraic numbers

More general, $\mathbb{A}=\{x\in\mathbb{R}:\; x\mbox{ & algebraic & over}\;\mathbb{Q}\}$ is a field (non finite extension of $\mathbb{Q}$)