Question

Write each polynomial in standard form. Then name each polynomial based on its degree and number of terms.
1. 5b^2 + 2n
2. -11d^4
3. 7a + 4 - a^2
4. 2x^3 - 9 + 2x + 8 - 4x

Answer 1

To write each polynomial in standard form, we need to arrange the terms in descending order of their degrees (the exponent of the variable). After arranging them, we can then name them based on their degree and number of terms.

1. **5b^2 + 2n**
- **Standard Form:** 5b^2 + 2n
- **Degree:** 2 (highest degree term is 5b²)
- **Number of Terms:** 2 (binomial)

2. **-11d^4**
- **Standard Form:** -11d^4
- **Degree:** 4 (highest degree term is -11d⁴)
- **Number of Terms:** 1 (monomial)

3. **7a + 4 - a^2**
- **Standard Form:** -a^2 + 7a + 4
- **Degree:** 2 (highest degree term is -a²)
- **Number of Terms:** 3 (trinomial)

4. **2x^3 - 9 + 2x + 8 - 4x**
- First, combine like terms:
- Combine 2x and -4x to get -2x.
- Combine -9 and 8 to get -1.
- Now, write in standard form:
- **Standard Form:** 2x^3 - 2x - 1
- **Degree:** 3 (highest degree term is 2x³)
- **Number of Terms:** 3 (trinomial)

Here’s the summary:
1. \(5b^2 + 2n\) - Degree 2, Binomial
2. \(-11d^4\) - Degree 4, Monomial
3. \(-a^2 + 7a + 4\) - Degree 2, Trinomial
4. \(2x^3 - 2x - 1\) - Degree 3, Trinomial