What is the Standard Form of the Polynomial Function.
Give also the Degree, Leading Term, and Classification of the Term and Degree.
• f(x) = 8a + a
• P(x) = 3a4b2c
Give also the Degree, Leading Term, and Classification of the Term and Degree.
• f(x) = 8a + a
• P(x) = 3a4b2c
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Answer:
The standard form of a polynomial function is expressed as the sum of terms in decreasing order of their degrees. Each term consists of a coefficient multiplied by one or more variables raised to certain powers.
We will analyze the given polynomial functions:
1. f(x) = 8a + a
- Standard Form: 9a
- Degree: The degree of a constant term like 9a is 0.
- Leading Term: The leading term is 9a since it has the highest degree.
- Classification: The term 9a is a monomial, which is a polynomial with a single term. The degree of this term is 0.
2. P(x) = 3a^4b^2c
- Standard Form: 3a^4b^2c
- Degree: The degree of the term 3a^4b^2c is determined by adding the exponents of each variable. The degree here is 4 + 2 + 1 = 7.
- Leading Term: The leading term is 3a^4b^2c since it has the highest degree.
- Classification: The term 3a^4b^2c is also a monomial, specifically a monomial of degree 7.
In summary:
1. f(x) = 9a (Degree: 0, Leading Term: 9a, Classification: Monomial of degree 0)
2. P(x) = 3a^4b^2c (Degree: 7, Leading Term: 3a^4b^2c, Classification: Monomial of degree 7)