Classify the polynomial 3X^2 - 4X + 7 based on its degree and number of terms.
Understand the Problem
The question is asking to categorize the polynomial 3X^2 - 4X + 7 based on two criteria: its degree, which is determined by the highest power of the variable, and the number of terms it contains.
Answer
The polynomial $3X^2 - 4X + 7$ is a quadratic trinomial.
Answer for screen readers
The polynomial $3X^2 - 4X + 7$ is a quadratic trinomial.
Steps to Solve
- Identify the degree of the polynomial
The degree of a polynomial is defined as the highest power of the variable in the expression.
In the polynomial $3X^2 - 4X + 7$, the term with the highest power is $3X^2$.
Hence, the degree is 2.
- Count the number of terms in the polynomial
The number of terms in a polynomial is simply how many separate expressions are present.
In the polynomial $3X^2 - 4X + 7$, we can see that there are three terms: $3X^2$, $-4X$, and $7$.
- Categorize based on the findings
Based on the degree and number of terms we identified, we can categorize:
- The polynomial is of degree 2, specifically called a "quadratic polynomial" since its degree is 2.
- It contains three terms, making it a "trinomial" since it has three terms.
The polynomial $3X^2 - 4X + 7$ is a quadratic trinomial.
More Information
Quadratic polynomials are commonly found in algebra, and they can be graphed as parabolas. Trinomials specifically have three terms and are important in factoring and solving equations.
Tips
- Misidentifying the degree by overlooking the highest power term. Always check all terms to find the maximum exponent.
- Miscounting the number of terms; make sure to separate individual terms by looking for "+" and "-" signs.
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