Question

Find the degree of the term -x^6 :

Find the degree of the term 1 :

Find the degree of the term -4x^7 :

Find the degree of the term -2x^4 :

Find the degree of the polynomial -x^6 +1 -4x^7-2x^4 :

Answer 1

To find the degree of each term and the polynomial, we follow the definition of a polynomial degree:

1. The **degree of a term** is the exponent of the variable in that term. If a term does not contain a variable, its degree is 0.

Now, let's evaluate each term:

1. **Term: -x^6**
- The degree is **6** (the exponent of x).

2. **Term: 1**
- This term does not contain any variable, so its degree is **0**.

3. **Term: -4x^7**
- The degree is **7** (the exponent of x).

4. **Term: -2x^4**
- The degree is **4** (the exponent of x).

Now, let's evaluate the degree of the polynomial:
\[-x^6 + 1 - 4x^7 - 2x^4\]

To find the degree of the polynomial, we look for the term with the highest degree:

- The degrees of the individual terms are:
- -x^6: 6
- 1: 0
- -4x^7: 7
- -2x^4: 4

The highest degree among these terms is **7** (from the term -4x^7).

Therefore, the degree of the polynomial \(-x^6 + 1 - 4x^7 - 2x^4\) is **7**.