Determine the degree of each of the following polynomials.
(i) $\frac{4 x-5 x^{2}+6 x^{3}}{2 x}$
(ii) $y^{2}\left(y-y^{3}\right)$
(iii) $(3 x-2)\left(2 x^{3}+3 x^{2}\right)$
(iv) $-\frac{1}{2} x+3$
(v) $-8$
(vi) $x^{-2}\left(x^{4}+x^{2}\right)$
(i) $\frac{4 x-5 x^{2}+6 x^{3}}{2 x}=\frac{4 x}{2 x}-\frac{5 x^{2}}{2 x}+\frac{6 x^{3}}{2 x}=2-\frac{5}{2} x+3 x^{2}$
Here, the highest power of $x$ is 2 . So, the degree of the polynomial is 2 .
(ii) $y^{2}\left(y-y^{3}\right)=y^{3}-y^{5}$
Here, the highest power of $y$ is 5 . So, the degree of the polynomial is 5 .
(iii) $(3 x-2)\left(2 x^{3}+3 x^{2}\right)=6 x^{4}+9 x^{3}-4 x^{3}-6 x^{2}=6 x^{4}+5 x^{3}-6 x^{2}$
Here, the highest power of $x$ is 4 . So, the degree of the polynomial is 4 .
(iv) $-\frac{1}{2} x+3$
Here, the highest power of $x$ is $1 .$ So, the degree of the polynomial is 1 .
(v) – 8
–8 is a constant polynomial. So, the degree of the polynomial is 0.
(vi) $x^{-2}\left(x^{4}+x^{2}\right)=x^{2}+x^{0}=x^{2}+1$
Here, the highest power of $x$ is 2 . So, the degree of the polynomial is 2 .
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