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

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