Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms. 3z^4-9z-7z^2
To write the polynomial in standard form, we need to arrange the terms in descending order of their exponents:
3z^4 - 7z^2 - 9z
To name the polynomial based on its degree and number of terms, we first count the number of terms, which is 3. Then we look at the highest exponent in the polynomial, which is 4. Therefore, this polynomial is a fourth-degree trinomial.
HI
To write the polynomial in standard form, we arrange the terms in descending order of their exponents.
The given polynomial is: 3z^4 - 7z^2 - 9z
Re-arranging the terms in descending order of exponents, we get:
3z^4 - 7z^2 - 9z
Now, let's determine the degree and number of terms in the polynomial.
The degree of a polynomial is the highest exponent of the variable. In this case, the highest exponent is 4, so the degree of the polynomial is 4.
The number of terms in a polynomial is the total count of individual terms separated by addition or subtraction. In this case, we have 3 terms: 3z^4, -7z^2, and -9z.
Therefore, the polynomial can be identified as a "fourth-degree trinomial" since it has a degree of 4 and contains three terms.
To write the polynomial in standard form, we arrange the terms in descending order of their exponents.
The given polynomial is:
3z^4 - 7z^2 - 9z
Rearranging the terms in descending order of exponents:
3z^4 - 7z^2 - 9z
Now, let's determine the name of the polynomial based on its degree and number of terms:
Degree: The degree of a polynomial is the highest exponent of the variable. In this case, the highest exponent is 4 (from the term 3z^4).
Number of terms: The number of terms in a polynomial refers to how many individual terms are present. In this case, we have three terms (3z^4, -7z^2, -9z).
Based on the degree and number of terms, we can name the polynomial as follows:
If the degree is 4 and there are 3 terms, it is called a "quartic trinomial."