Question

# To calculate: the coefficient and the degree of each term of the polynomial 18x^{2}+36x^{9}-7x+3 and then find the degree of the polynomial.

Polynomial arithmetic
To calculate: The coefficient and the degree of each term of the polynomial $$\displaystyle{18}{x}^{{{2}}}+{36}{x}^{{{9}}}-{7}{x}+{3}$$ and then find the degree of the polynomial.

2021-08-07

Step 1
Consider the poynomial.
$$\displaystyle{18}{x}^{{{3}}}+{36}{x}^{{{9}}}-{7}{x}+{3}$$
Since, the terms are saparated by addition signs, the terms are listed as follows:
$$\displaystyle{18}{x}^{{{3}}},\ {36}{x}^{{{9}}},\ -{7}{x}$$ and 3
Thus, the terms of the polynomial
$$\displaystyle{18}{x}^{{{3}}}+{36}{x}^{{{9}}}-{7}{x}+{3}$$ are $$\displaystyle{18}{x}^{{{3}}},\ {36}{x}^{{{9}}},\ -{7}{x}$$ and 3.
The coefficients of each term of the polynomial
$$\displaystyle{18}{x}^{{{3}}}+{36}{x}^{{{9}}}-{7}{x}+{3}$$ are $$\displaystyle{18},\ {36},\ -{7}$$ and 3.
The degree of each term of the polynomial $$\displaystyle{18}{x}^{{{3}}}+{36}{x}^{{{9}}}-{7}{x}+{3}$$ add $$3,\ 9,\ 1,$$ and 0.
The degree of the polynomial $$\displaystyle{18}{x}^{{{3}}}+{36}{x}^{{{9}}}-{7}{x}+{3}$$ is 9.