Let's analyze the given polynomial: [tex]\( 4 - 7q^3 \)[/tex].
1. Write the polynomial in standard form:
- The standard form of a polynomial arranges the terms in descending order of the powers of the variable [tex]\( q \)[/tex].
- In this polynomial, the term with the highest power is [tex]\( -7q^3 \)[/tex].
- Thus, we write the polynomial in standard form by placing [tex]\( -7q^3 \)[/tex] first, followed by the constant term [tex]\( 4 \)[/tex].
Therefore, the standard form is:
[tex]\[
-7q^3 + 4
\][/tex]
2. Identify the degree of the polynomial:
- The degree of a polynomial is the highest power of the variable [tex]\( q \)[/tex] present in the polynomial.
- Here, the highest power of [tex]\( q \)[/tex] is [tex]\( 3 \)[/tex], found in the term [tex]\( -7q^3 \)[/tex].
Thus, the degree is:
[tex]\[
3
\][/tex]
3. Identify the leading coefficient:
- The leading coefficient is the coefficient of the term with the highest power of [tex]\( q \)[/tex].
- In this polynomial, the term with the highest power (degree 3) is [tex]\( -7q^3 \)[/tex], and its coefficient is [tex]\( -7 \)[/tex].
Thus, the leading coefficient is:
[tex]\[
-7
\][/tex]
4. Classify the polynomial by the number of terms:
- The number of terms in a polynomial affects its classification.
- In the given polynomial [tex]\( 4 - 7q^3 \)[/tex], there are two distinct terms: [tex]\( 4 \)[/tex] and [tex]\( -7q^3 \)[/tex].
Since a polynomial with two terms is called a binomial, we classify this polynomial as a:
[tex]\[
\text{binomial}
\][/tex]
In summary:
- Standard form: [tex]\(-7q^3 + 4\)[/tex]
- Degree: 3
- Leading coefficient: -7
- Classification by the number of terms: Binomial
