write the polynomial in standard form. Then name the polynomial based on its degree and number of terms.

8x + 5x^3 -5

Sure, here's the polynomial in standard form:

5x^3 + 8x - 5.

Based on its degree and number of terms, we can call this polynomial a trinomial of degree 3. However, if you're in the mood for a little humor, you could also call it the "Almost Symmetrical Confetti Polynomial" because it's close to being symmetrical, but the -5 at the end decides to crash the party in the name of chaos. Keep it lively, right?

To write the polynomial in standard form, we need to arrange the terms in descending order of the degree.

Rewriting the polynomial in descending order:

5x^3 + 8x - 5

Now let's determine the name of the polynomial based on its degree and number of terms.
- The highest exponent in the polynomial is 3, which indicates the degree of the polynomial is 3.
- The polynomial has 3 terms: 5x^3, 8x, and -5.

Based on this information, we can say that the polynomial is a cubic trinomial.

To write the polynomial in standard form, we need to rearrange the terms in descending order of exponents.

The given polynomial is: 8x + 5x^3 - 5

Rearranging the terms in descending order of exponents, we get: 5x^3 + 8x - 5

Now, let's determine the degree and number of terms of the polynomial:

Degree: The degree of a polynomial is the highest exponent of the variable. In this case, the highest exponent is 3 (from the term 5x^3). Therefore, the degree of the polynomial is 3.

Number of terms: Counting the number of terms in the polynomial, we have 3 terms: 5x^3, 8x, and -5.

Based on its degree and number of terms, we can name the polynomial as follows:

Degree:
- The polynomial has a degree of 3.

Number of terms:
- The polynomial has 3 terms.

Combining the degree and number of terms, we can name the polynomial as a "cubic polynomial" since it has a degree of 3 and 3 terms.

descending exponents:

5x^3 + 8x - 3
degree: highest power = 3
terms are separated by + and - signs, so ...