Classify the polynomial by degree and by number of terms. 3x² The polynomial is a quadratic trinomial. cubic constant quadratic linear
The Correct Answer and Explanation is :
The given polynomial is 3x². Let’s classify it based on its degree and number of terms.
Step 1: Classifying by Degree
The degree of a polynomial is determined by the highest power of the variable (x) in the expression.
- In 3x², the exponent of x is 2.
- A polynomial with a degree of 2 is called a quadratic polynomial.
Thus, 3x² is a quadratic polynomial.
Step 2: Classifying by Number of Terms
The number of terms in a polynomial is determined by counting the individual terms separated by addition or subtraction.
- 3x² consists of only one term.
- A polynomial with one term is called a monomial.
Thus, 3x² is a quadratic monomial.
Step 3: Correcting the Misclassification
The original classification stated that 3x² is a quadratic trinomial, which is incorrect because:
- A trinomial must have exactly three terms.
- 3x² only has one term.
The correct classification of 3x² is:
- Degree: Quadratic (since the highest exponent is 2).
- Number of terms: Monomial (since there is only one term).
Final Answer:
3x² is a quadratic monomial.
Additional Explanation:
Here are some other classifications for reference:
- Linear Polynomial: Highest exponent is 1 (e.g., 2x + 5).
- Quadratic Polynomial: Highest exponent is 2 (e.g., x² – 4x + 3).
- Cubic Polynomial: Highest exponent is 3 (e.g., x³ + 2x² – x + 7).
- Monomial: One term (e.g., 5x²).
- Binomial: Two terms (e.g., x² + 4x).
- Trinomial: Three terms (e.g., x² – 3x + 2).
Hope this helps! 🚀