Questions: Find the degree of the term -6 x^8 : Find the degree of the term 1 : Find the degree of the term -5 x^7 : Find the degree of the term -3 x^5 : Find the degree of the polynomial -6 x^8+1-5 x^7-3 x^5 :

Find the degree of the term -6 x^8 :
Find the degree of the term 1 :
Find the degree of the term -5 x^7 :
Find the degree of the term -3 x^5 :
Find the degree of the polynomial -6 x^8+1-5 x^7-3 x^5 :

Transcript text: Find the degree of the term $-6 x^{8}$ : $\square$ Find the degree of the term 1 : $\square$ Find the degree of the têrm $-5 x^{7}$ : $\square$ Find the degree of the term $-3 x^{5}$ : $\square$ Find the degree of the polynomial $-6 x^{8}+1-5 x^{7}-3 x^{5}$ : $\square$

Solution

Solution Steps

To find the degree of a term, we look at the exponent of the variable in that term. For a polynomial, the degree is the highest degree of its terms.

For the term $-6x^8$, the degree is 8.
For the term 1, the degree is 0 (since it can be written as $1x^0$).
For the term $-5x^7$, the degree is 7.
For the term $-3x^5$, the degree is 5.
For the polynomial $-6x^8 + 1 - 5x^7 - 3x^5$, the degree is the highest degree among its terms, which is 8.

Step 1: Degree of the Term $-6x^8$

The degree of the term $-6x^8$ is determined by the exponent of $x$, which is $8$. Thus, we have: \[ \text{Degree of } -6x^8 = 8 \]

Step 2: Degree of the Term $1$

The term $1$ can be expressed as $1x^0$, where the exponent is $0$. Therefore, the degree is: \[ \text{Degree of } 1 = 0 \]

Step 3: Degree of the Term $-5x^7$

For the term $-5x^7$, the degree is given by the exponent of $x$, which is $7$. Hence, we find: \[ \text{Degree of } -5x^7 = 7 \]