Math / Algebra

QuestionIdentify the degree of the terms and the degree of the polynomial. $2 a b^{9}-8 a^{7}+8 b^{2}-6$
What is the degree of the first term, $2 a b^{9}$ ? $\square$

Studdy Solution

STEP 1

1. The degree of a term in a polynomial is the sum of the exponents of the variables in that term.
2. The degree of a polynomial is the highest degree of any term in the polynomial.

STEP 2

1. Identify the degree of each term in the polynomial.
2. Determine the degree of the polynomial.
3. Identify the degree of the first term, $2ab^9$ .

STEP 3

Identify the degree of each term in the polynomial:
- For the term $2ab^9$ , the degree is the sum of the exponents of $a$ and $b$ . Here, $a$ has an exponent of 1 and $b$ has an exponent of 9.
$\text{Degree of } 2ab^9 = 1 + 9 = 10$

STEP 4

- For the term $-8a^7$ , the degree is the exponent of $a$ , which is 7.
$\text{Degree of } -8a^7 = 7$

STEP 5

- For the term $8b^2$ , the degree is the exponent of $b$ , which is 2.
$\text{Degree of } 8b^2 = 2$

STEP 6

- For the constant term $-6$ , the degree is 0 because there are no variables.
$\text{Degree of } -6 = 0$

STEP 7

Determine the degree of the polynomial by identifying the highest degree among all the terms:
The degrees of the terms are 10, 7, 2, and 0. The highest degree is 10.
$\text{Degree of the polynomial} = 10$

STEP 8

Identify the degree of the first term, $2ab^9$ :
As calculated earlier, the degree of $2ab^9$ is 10.
$\text{Degree of the first term} = \boxed{10}$
The degree of the first term, $2ab^9$ , is $\boxed{10}$ .

Was this helpful?

QuestionIdentify the degree of the terms and the degree of the polynomial. $2 a b^{9}-8 a^{7}+8 b^{2}-6$
What is the degree of the first term, $2 a b^{9}$ ? $\square$

Studdy Solution

STEP 1

1. The degree of a term in a polynomial is the sum of the exponents of the variables in that term.
2. The degree of a polynomial is the highest degree of any term in the polynomial.

STEP 2

1. Identify the degree of each term in the polynomial.
2. Determine the degree of the polynomial.
3. Identify the degree of the first term, $2ab^9$ .

STEP 3

Identify the degree of each term in the polynomial:
- For the term $2ab^9$ , the degree is the sum of the exponents of $a$ and $b$ . Here, $a$ has an exponent of 1 and $b$ has an exponent of 9.
$\text{Degree of } 2ab^9 = 1 + 9 = 10$

STEP 4

- For the term $-8a^7$ , the degree is the exponent of $a$ , which is 7.
$\text{Degree of } -8a^7 = 7$

STEP 5

- For the term $8b^2$ , the degree is the exponent of $b$ , which is 2.
$\text{Degree of } 8b^2 = 2$

STEP 6

- For the constant term $-6$ , the degree is 0 because there are no variables.
$\text{Degree of } -6 = 0$

STEP 7

Determine the degree of the polynomial by identifying the highest degree among all the terms:
The degrees of the terms are 10, 7, 2, and 0. The highest degree is 10.
$\text{Degree of the polynomial} = 10$

STEP 8

Identify the degree of the first term, $2ab^9$ :
As calculated earlier, the degree of $2ab^9$ is 10.
$\text{Degree of the first term} = \boxed{10}$
The degree of the first term, $2ab^9$ , is $\boxed{10}$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionIdentify the degree of the terms and the degree of the polynomial. 2ab9−8a7+8b2−62 a b^{9}-8 a^{7}+8 b^{2}-62ab9−8a7+8b2−6What is the degree of the first term, 2ab92 a b^{9}2ab9 ? □\square□

Studdy Solution

STEP 1

1. The degree of a term in a polynomial is the sum of the exponents of the variables in that term.2. The degree of a polynomial is the highest degree of any term in the polynomial.

STEP 2

1. Identify the degree of each term in the polynomial.2. Determine the degree of the polynomial.3. Identify the degree of the first term, 2ab92ab^92ab9.

STEP 3

Identify the degree of each term in the polynomial:- For the term 2ab92ab^92ab9, the degree is the sum of the exponents of aaa and bbb. Here, aaa has an exponent of 1 and bbb has an exponent of 9.Degree of 2ab9=1+9=10 \text{Degree of } 2ab^9 = 1 + 9 = 10 Degree of 2ab9=1+9=10

STEP 4

- For the term −8a7-8a^7−8a7, the degree is the exponent of aaa, which is 7.Degree of −8a7=7 \text{Degree of } -8a^7 = 7 Degree of −8a7=7

STEP 5

- For the term 8b28b^28b2, the degree is the exponent of bbb, which is 2.Degree of 8b2=2 \text{Degree of } 8b^2 = 2 Degree of 8b2=2

STEP 6

- For the constant term −6-6−6, the degree is 0 because there are no variables.Degree of −6=0 \text{Degree of } -6 = 0 Degree of −6=0

STEP 7

Determine the degree of the polynomial by identifying the highest degree among all the terms:The degrees of the terms are 10, 7, 2, and 0. The highest degree is 10.Degree of the polynomial=10 \text{Degree of the polynomial} = 10 Degree of the polynomial=10

STEP 8

Identify the degree of the first term, 2ab92ab^92ab9:As calculated earlier, the degree of 2ab92ab^92ab9 is 10.Degree of the first term=10 \text{Degree of the first term} = \boxed{10} Degree of the first term=10​ The degree of the first term, 2ab92ab^92ab9, is 10 \boxed{10} 10​.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionIdentify the degree of the terms and the degree of the polynomial. $2 a b^{9}-8 a^{7}+8 b^{2}-6$
What is the degree of the first term, $2 a b^{9}$ ? $\square$

1. The degree of a term in a polynomial is the sum of the exponents of the variables in that term.
2. The degree of a polynomial is the highest degree of any term in the polynomial.

1. Identify the degree of each term in the polynomial.
2. Determine the degree of the polynomial.
3. Identify the degree of the first term, $2ab^9$ .

Identify the degree of each term in the polynomial:
- For the term $2ab^9$ , the degree is the sum of the exponents of $a$ and $b$ . Here, $a$ has an exponent of 1 and $b$ has an exponent of 9.
$\text{Degree of } 2ab^9 = 1 + 9 = 10$

- For the term $-8a^7$ , the degree is the exponent of $a$ , which is 7.
$\text{Degree of } -8a^7 = 7$

- For the term $8b^2$ , the degree is the exponent of $b$ , which is 2.
$\text{Degree of } 8b^2 = 2$

- For the constant term $-6$ , the degree is 0 because there are no variables.
$\text{Degree of } -6 = 0$

Determine the degree of the polynomial by identifying the highest degree among all the terms:
The degrees of the terms are 10, 7, 2, and 0. The highest degree is 10.
$\text{Degree of the polynomial} = 10$

Identify the degree of the first term, $2ab^9$ :
As calculated earlier, the degree of $2ab^9$ is 10.
$\text{Degree of the first term} = \boxed{10}$
The degree of the first term, $2ab^9$ , is $\boxed{10}$ .