Question

# Identify the degree of each term of the polynomial and the degree of the polynomial. -5x^{3}+5x^{2}+\frac{6}{7x}+4

Applications of integrals
Identify the degree of each term of the polynomial and the degree of the polynomial.
$$\displaystyle-{5}{x}^{{{3}}}+{5}{x}^{{{2}}}+{\frac{{{6}}}{{{7}{x}}}}+{4}$$

2021-03-25
Step 1
Given information-
We have a polynomial equation-
$$\displaystyle-{5}{x}^{{{3}}}+{5}{x}^{{{2}}}+{\frac{{{6}}}{{{7}{x}}}}+{4}$$
We have to find the degree of each term and the degree of the polynomial.
The degree of a polynomial is the highest power of its terms.
The power of a term is the sum of the exponents of the variables that appear in it.
Step 2
So,
The degree of the term $$\displaystyle-{5}{x}^{{{3}}}={3}$$
Degree of $$\displaystyle{5}{x}^{{{2}}}={2}$$
Degree of $$\displaystyle{\frac{{{6}}}{{{7}{x}}}}={1}$$
Degree of 4 = 0
And the degree of the polynomial is-
$$\displaystyle-{5}{x}^{{{3}}}+{5}{x}^{{{2}}}+{\frac{{{6}}}{{{7}{x}}}}+{4}={3}$$
Therefore the answers are-
3, 2, 1, 0, and 3