Write the degree of each of the following polynomials:
$x^{5} y^{6} - 7 x^{3} y^{10} + 20 x^{5} y^{6} z^{5}$

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Solution

The degree of a polynomial is the highest of the degrees of its monomials with non-zero coefficients.
Finding degrees for each term:
First term $x^{5} y^{6} = 5 + 6 = 11$
Second term $(- 7 x^{3} y^{10}) = 3 + 10 = 13$
Third term $20 x^{5} y^{6} z^{5} = 5 + 6 + 5 = 16$
It is observed that the highest power is $16$
$∴$ Degree of the polynomial $= 16$

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