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
ANSWERED
asked 2021-08-06
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.

Answers (1)

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.

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