Question
Classify the polynomial: \( 4x^{2} - 7x + 3 \) as a monomial, binomial, or trinomial.
Ask by Pearson Spencer. in India
Jan 21,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 4x^{2} - 7x + 3 \) is a trinomial.
Solution
The polynomial \( 4x^{2} - 7x + 3 \) can be classified based on the number of terms it contains. Here's how the classification works:
1. **Monomial**: A polynomial with **one term**.
- *Example*: \( 5x^{3} \)
2. **Binomial**: A polynomial with **two terms**.
- *Example*: \( 4x^{2} - 7x \)
3. **Trinomial**: A polynomial with **three terms**.
- *Example*: \( 4x^{2} - 7x + 3 \)
**Classification of \( 4x^{2} - 7x + 3 \):**
- **Number of Terms**: Three (\(4x^{2}\), \(-7x\), and \(+3\))
- **Type**: **Trinomial**
Therefore, \( 4x^{2} - 7x + 3 \) is classified as a **trinomial**.
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Simplify this solution The Deep Dive
The polynomial \( 4x^{2} - 7x + 3 \) is classified as a trinomial because it contains three terms: \( 4x^{2} \), \( -7x \), and \( 3 \). Each of these terms is separate, and together they form a complete expression. Trinomials like this one come in handy in various areas of mathematics, especially in factoring and solving quadratics. It’s quite common to see trinomials in algebraic equations, and mastering their classification helps in simplifying and solving higher-level problems.
