College

Find the degree of the term [tex]$4x^9$[/tex]: [tex]\square[/tex]

Find the degree of the term 3: [tex]\square[/tex]

Find the degree of the term [tex]$5x^8$[/tex]: [tex]\square[/tex]

Find the degree of the term [tex]$-5x^6$[/tex]: [tex]\square[/tex]

Find the degree of the polynomial [tex]$4x^9 + 3 + 5x^8 - 5x^6$[/tex]: [tex]\square[/tex]

Answer :

Sure! Let's go through each part of the question step by step:

1. Find the degree of the term [tex]\(4x^9\)[/tex]:

- A term's degree is the exponent of the variable in that term.
- In [tex]\(4x^9\)[/tex], the exponent of [tex]\(x\)[/tex] is 9.
- So, the degree of the term [tex]\(4x^9\)[/tex] is 9.

2. Find the degree of the term 3:

- A constant term like 3 does not have a variable attached to it.
- By convention, the degree of a constant term is 0.
- So, the degree of the term 3 is 0.

3. Find the degree of the term [tex]\(5x^8\)[/tex]:

- The degree of a term is given by the exponent of the variable.
- Here, in [tex]\(5x^8\)[/tex], the exponent of [tex]\(x\)[/tex] is 8.
- Thus, the degree of the term [tex]\(5x^8\)[/tex] is 8.

4. Find the degree of the term [tex]\(-5x^6\)[/tex]:

- The exponent of the variable in a term determines its degree.
- In [tex]\(-5x^6\)[/tex], the exponent of [tex]\(x\)[/tex] is 6.
- Therefore, the degree of the term [tex]\(-5x^6\)[/tex] is 6.

5. Find the degree of the polynomial [tex]\(4x^9 + 3 + 5x^8 - 5x^6\)[/tex]:

- To find the degree of a polynomial, look for the term with the highest degree among all its terms.
- From the degrees we found above: [tex]\(9\)[/tex] (from [tex]\(4x^9\)[/tex]), [tex]\(0\)[/tex] (from 3), [tex]\(8\)[/tex] (from [tex]\(5x^8\)[/tex]), and [tex]\(6\)[/tex] (from [tex]\(-5x^6\)[/tex]).
- The highest degree is 9.
- Therefore, the degree of the polynomial is 9.

I hope this helps you understand how to find the degree of terms and polynomials! If you have any more questions, feel free to ask.