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.
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4$\begingroup$ What's the book? $\endgroup$– Andrew ChinNov 10, 2019 at 5:52
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2 Answers
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It depends.
$(1 + x^2)^2$ 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 $\mathbb{R}[1 + x^2]$.
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$\begingroup$ So do u mean ,if the polynomial was equal to f(x),the answer is 4,and 2 if it was f(x^2)? $\endgroup$ Nov 10, 2019 at 6:20
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$$(1+x^2)^2 = x^4+2x^2+1$$ is a polynomial of degree $4$ so obviously the book's answer is wrong.
answered Nov 10, 2019 at 5:56