Math / Algebra

Question1. $m^{5} n^{2}+m n^{2}+n^{6}$ The degree of the polynomial is 5 The degree of the polynomial is 6 The degree of the polynomial is 7 The polynomial is a monomial The polynomial is a binomial The polynomial is a trinomial

Studdy Solution

STEP 1

1. A polynomial is an expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication.
2. The degree of a polynomial is the highest power of the variable in the polynomial.
3. A monomial is a polynomial with only one term.
4. A binomial is a polynomial with exactly two terms.
5. A trinomial is a polynomial with exactly three terms.

STEP 2

1. Identify the degree of the given polynomial.
2. Classify the polynomial as a monomial, binomial, or trinomial.

STEP 3

Identify the degree of the term $m^5 n^2$ .
The degree of a term is the sum of the exponents of its variables. $\text{Degree of } m^5 n^2 = 5 + 2 = 7$

STEP 4

Identify the degree of the term $m n^2$ .
$\text{Degree of } m n^2 = 1 + 2 = 3$

STEP 5

Identify the degree of the term $n^6$ .
$\text{Degree of } n^6 = 6$

STEP 6

Determine the degree of the polynomial $m^5 n^2 + m n^2 + n^6$ .
The degree of the polynomial is the highest degree among its terms. $\text{Degree of the polynomial } = \max(7, 3, 6) = 7$

STEP 7

Classify the polynomial $m^5 n^2 + m n^2 + n^6$ .
Count the number of terms in the polynomial. $\text{Number of terms} = 3$
Since the polynomial has three terms, it is classified as a trinomial.
Solution: The degree of the polynomial $m^5 n^2 + m n^2 + n^6$ is 7. The polynomial is a trinomial.

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Question1. $m^{5} n^{2}+m n^{2}+n^{6}$ The degree of the polynomial is 5 The degree of the polynomial is 6 The degree of the polynomial is 7 The polynomial is a monomial The polynomial is a binomial The polynomial is a trinomial

Studdy Solution

STEP 1

STEP 2

1. Identify the degree of the given polynomial.
2. Classify the polynomial as a monomial, binomial, or trinomial.

STEP 3

Identify the degree of the term $m^5 n^2$ .
The degree of a term is the sum of the exponents of its variables. $\text{Degree of } m^5 n^2 = 5 + 2 = 7$

STEP 4

Identify the degree of the term $m n^2$ .
$\text{Degree of } m n^2 = 1 + 2 = 3$

STEP 5

Identify the degree of the term $n^6$ .
$\text{Degree of } n^6 = 6$

STEP 6

Determine the degree of the polynomial $m^5 n^2 + m n^2 + n^6$ .
The degree of the polynomial is the highest degree among its terms. $\text{Degree of the polynomial } = \max(7, 3, 6) = 7$

STEP 7

Classify the polynomial $m^5 n^2 + m n^2 + n^6$ .
Count the number of terms in the polynomial. $\text{Number of terms} = 3$
Since the polynomial has three terms, it is classified as a trinomial.
Solution: The degree of the polynomial $m^5 n^2 + m n^2 + n^6$ is 7. The polynomial is a trinomial.

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Question1. m5n2+mn2+n6m^{5} n^{2}+m n^{2}+n^{6}m5n2+mn2+n6 The degree of the polynomial is 5 The degree of the polynomial is 6 The degree of the polynomial is 7 The polynomial is a monomial The polynomial is a binomial The polynomial is a trinomial

Studdy Solution

STEP 1

STEP 2

1. Identify the degree of the given polynomial.2. Classify the polynomial as a monomial, binomial, or trinomial.

STEP 3

Identify the degree of the term m5n2m^5 n^2m5n2.The degree of a term is the sum of the exponents of its variables. Degree of m5n2=5+2=7 \text{Degree of } m^5 n^2 = 5 + 2 = 7 Degree of m5n2=5+2=7

STEP 4

Identify the degree of the term mn2m n^2mn2.Degree of mn2=1+2=3 \text{Degree of } m n^2 = 1 + 2 = 3 Degree of mn2=1+2=3

STEP 5

Identify the degree of the term n6n^6n6.Degree of n6=6 \text{Degree of } n^6 = 6 Degree of n6=6

STEP 6

Determine the degree of the polynomial m5n2+mn2+n6m^5 n^2 + m n^2 + n^6m5n2+mn2+n6.The degree of the polynomial is the highest degree among its terms. Degree of the polynomial =max⁡(7,3,6)=7 \text{Degree of the polynomial } = \max(7, 3, 6) = 7 Degree of the polynomial =max(7,3,6)=7

STEP 7

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Question1. $m^{5} n^{2}+m n^{2}+n^{6}$ The degree of the polynomial is 5 The degree of the polynomial is 6 The degree of the polynomial is 7 The polynomial is a monomial The polynomial is a binomial The polynomial is a trinomial

1. Identify the degree of the given polynomial.
2. Classify the polynomial as a monomial, binomial, or trinomial.

Identify the degree of the term $m^5 n^2$ .
The degree of a term is the sum of the exponents of its variables. $\text{Degree of } m^5 n^2 = 5 + 2 = 7$

Identify the degree of the term $m n^2$ .
$\text{Degree of } m n^2 = 1 + 2 = 3$

Identify the degree of the term $n^6$ .
$\text{Degree of } n^6 = 6$

Determine the degree of the polynomial $m^5 n^2 + m n^2 + n^6$ .
The degree of the polynomial is the highest degree among its terms. $\text{Degree of the polynomial } = \max(7, 3, 6) = 7$