# What is the degree of the polynomial $(1+x^2)^2$?

Somewhere I read that the degree of any polynomial means the highest power of the variable .According to that, the answer should be 4. But one of my books that had this problem said that the answer is 2. I don't understand why it will be 2 and not 4.

• What's the book? Nov 10 '19 at 5:52

$$(1 + x^2)^2$$ is a polynomial of degree $$4$$ in $$x$$, but also a polynomial of degree $$2$$ in $$1 + x^2$$. More formally, if the field is $$\mathbb{R}$$, then $$(1 + x^2)^2$$ has degree $$4$$ in $$\mathbb{R}[x]$$, but has degree $$2$$ in $$\mathbb{R}[1 + x^2]$$.
$$(1+x^2)^2 = x^4+2x^2+1$$ is a polynomial of degree $$4$$ so obviously the book's answer is wrong.