What is the degree of the polynomial function f(x) = 3x - x^3 + 4x^2 - 5?
Understand the Problem
The question is asking for the degree of a given polynomial function, which means we need to identify the highest exponent of its variables.
Answer
The degree of the polynomial is $3$.
Answer for screen readers
The degree of the polynomial function $f(x) = 3x - x^3 + 4x^2 - 5$ is $3$.
Steps to Solve
- Identify individual terms of the polynomial
The polynomial function is given as $f(x) = 3x - x^3 + 4x^2 - 5$. We can break it down into its individual terms:
- $3x$
- $-x^3$
- $4x^2$
- $-5$
- Determine the degree of each term
Next, we look at each term to find its degree:
- The term $3x$ has a degree of $1$ (since $x$ is raised to the power of 1).
- The term $-x^3$ has a degree of $3$ (since $x$ is raised to the power of 3).
- The term $4x^2$ has a degree of $2$ (since $x$ is raised to the power of 2).
- The constant term $-5$ has a degree of $0$ (constants are considered as degree 0).
- Identify the highest degree
Now, we compare the degrees we found:
- $1$ (from $3x$)
- $3$ (from $-x^3$)
- $2$ (from $4x^2$)
- $0$ (from $-5$)
The highest degree is $3$.
The degree of the polynomial function $f(x) = 3x - x^3 + 4x^2 - 5$ is $3$.
More Information
The degree of a polynomial is determined by the term with the highest exponent. In this case, the term $-x^3$ dictates that the degree is $3$.
Tips
- Choosing a term without considering all terms: Sometimes, one might only look at the first term and inaccurately identify the degree as $1$ instead of checking all terms to find the highest exponent.
- Forgetting that constants have a degree of $0$: It's easy to overlook that constant terms do not contribute to the degree.
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