Question

1. Explain in detail why the degree of the expression below is not 6.

3x^2+6〖xy-10x^5+y^6-10x^3 y^5〗^

Answer 1

bear in mind that, the degree of a term, comes from the sum of exponents of its variables, and degree of the polynomial, is the highest from all terms,


`\bf 3x^2+6[xy-10x^5+y^2-10x^3y^5] \\\\\\ 3x^2+6xy-60x^5+6y^2-60x^3y^5 \\\\\\ \textit{let's check the degree of every term}\quad \begin{cases} 3x^2&de gree~2\\\\ 6x^1y^1&1+1\\ &de gree~2\\\\ 60x^5&de gree~5\\\\ 6y^2&de gree~2\\\\ 60x^3y^5&3+5\\ &de gree~8 \end{cases}`