Math / Algebra

QuestionIdentify the degree of the terms and the degree of the polynomial. $8 a^{3} b-2 a^{7}+6 b^{8}-6$
What is the degree of the first term, $8 a^{3} b$ ? 4 What is the degree of the second term, $-2 a^{7}$ ? 7 What is the degree of the third term, $6 \mathrm{~b}^{8}$ ? 8 What is the degree of the fourth term, -6 ?

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 its terms.

STEP 2

1. Identify the degree of each term.
2. Determine the degree of the polynomial.

STEP 3

Identify the degree of the first term, $8a^3b$ .
The term $8a^3b$ has variables $a$ and $b$ with exponents 3 and 1, respectively.
Degree of the term = $3 + 1 = 4$ .

STEP 4

Identify the degree of the second term, $-2a^7$ .
The term $-2a^7$ has the variable $a$ with an exponent of 7.
Degree of the term = $7$ .

STEP 5

Identify the degree of the third term, $6b^8$ .
The term $6b^8$ has the variable $b$ with an exponent of 8.
Degree of the term = $8$ .

STEP 6

Identify the degree of the fourth term, $-6$ .
The term $-6$ is a constant term with no variables.
Degree of the term = $0$ .

STEP 7

Determine the degree of the polynomial.
The degrees of the terms are 4, 7, 8, and 0.
The degree of the polynomial is the highest of these degrees, which is $8$ .
The degree of the polynomial is $\boxed{8}$ .

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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 its terms.

STEP 2

1. Identify the degree of each term.
2. Determine the degree of the polynomial.

STEP 3

Identify the degree of the first term, $8a^3b$ .
The term $8a^3b$ has variables $a$ and $b$ with exponents 3 and 1, respectively.
Degree of the term = $3 + 1 = 4$ .

STEP 4

Identify the degree of the second term, $-2a^7$ .
The term $-2a^7$ has the variable $a$ with an exponent of 7.
Degree of the term = $7$ .

STEP 5

Identify the degree of the third term, $6b^8$ .
The term $6b^8$ has the variable $b$ with an exponent of 8.
Degree of the term = $8$ .

STEP 6

Identify the degree of the fourth term, $-6$ .
The term $-6$ is a constant term with no variables.
Degree of the term = $0$ .

STEP 7

Determine the degree of the polynomial.
The degrees of the terms are 4, 7, 8, and 0.
The degree of the polynomial is the highest of these degrees, which is $8$ .
The degree of the polynomial is $\boxed{8}$ .

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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 its terms.

STEP 2

1. Identify the degree of each term.2. Determine the degree of the polynomial.

STEP 3

Identify the degree of the first term, 8a3b8a^3b8a3b.The term 8a3b8a^3b8a3b has variables aaa and bbb with exponents 3 and 1, respectively.Degree of the term = 3+1=43 + 1 = 43+1=4.

STEP 4

Identify the degree of the second term, −2a7-2a^7−2a7.The term −2a7-2a^7−2a7 has the variable aaa with an exponent of 7.Degree of the term = 777.

STEP 5

Identify the degree of the third term, 6b86b^86b8.The term 6b86b^86b8 has the variable bbb with an exponent of 8.Degree of the term = 888.

STEP 6

Identify the degree of the fourth term, −6-6−6.The term −6-6−6 is a constant term with no variables.Degree of the term = 000.

STEP 7

Determine the degree of the polynomial.The degrees of the terms are 4, 7, 8, and 0.The degree of the polynomial is the highest of these degrees, which is 888. The degree of the polynomial is 8 \boxed{8} 8​.

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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 its terms.

1. Identify the degree of each term.
2. Determine the degree of the polynomial.

Identify the degree of the first term, $8a^3b$ .
The term $8a^3b$ has variables $a$ and $b$ with exponents 3 and 1, respectively.
Degree of the term = $3 + 1 = 4$ .

Identify the degree of the second term, $-2a^7$ .
The term $-2a^7$ has the variable $a$ with an exponent of 7.
Degree of the term = $7$ .

Identify the degree of the third term, $6b^8$ .
The term $6b^8$ has the variable $b$ with an exponent of 8.
Degree of the term = $8$ .

Identify the degree of the fourth term, $-6$ .
The term $-6$ is a constant term with no variables.
Degree of the term = $0$ .

Determine the degree of the polynomial.
The degrees of the terms are 4, 7, 8, and 0.
The degree of the polynomial is the highest of these degrees, which is $8$ .
The degree of the polynomial is $\boxed{8}$ .