QuestionIs the expression $-\frac{c}{5}+9 c^{3} d^{4}+c^{2} d^{3}$ a polynomial? If yes, identify its type and degree.

Studdy Solution

STEP 1

Assumptions1. We are given the expression $-\frac{c}{5}+9 c^{3} d^{4}+c^{} d^{3}$ . . We need to determine if this expression is a polynomial or not.
3. If it is a polynomial, we need to state the type and degree of the polynomial.

STEP 2

A polynomial is an algebraic expression that can have one or more terms, but each term must be a product of a constant and a variable raised to a non-negative integer exponent.

STEP 3

Let's examine each term of the given expression to see if it meets the criteria of a polynomial.
The first term is $-\frac{c}{5}$ , which is the product of a constant and a variable raised to the power of1. This term meets the criteria.

STEP 4

The second term is $9 c^{3} d^{4}$ , which is the product of a constant and variables raised to non-negative integer exponents. This term meets the criteria.

STEP 5

The third term is $c^{2} d^{3}$ , which is the product of a constant (in this case,1) and variables raised to non-negative integer exponents. This term meets the criteria.

STEP 6

Since all terms of the given expression meet the criteria of a polynomial, we can conclude that the expression $-\frac{c}{5}+9 c^{3} d^{4}+c^{2} d^{3}$ is a polynomial.

STEP 7

Now, we need to determine the type and degree of the polynomial. The type of a polynomial is determined by the number of terms it has. Our polynomial has three terms, so it is a trinomial.

STEP 8

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

STEP 9

The first term, $-\frac{c}{5}$ , has a total degree of.

STEP 10

The second term, $9 c^{3} d^{4}$ , has a total degree of $3+4=7$ .

STEP 11

The third term, $c^{} d^{3}$ , has a total degree of $+3=5$ .

STEP 12

The highest total degree among all terms is7, so the degree of the polynomial is7.
The given expression $-\frac{c}{5}+9 c^{} d^{4}+c^{2} d^{}$ is a trinomial of degree7.

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QuestionIs the expression $-\frac{c}{5}+9 c^{3} d^{4}+c^{2} d^{3}$ a polynomial? If yes, identify its type and degree.

Studdy Solution

STEP 1

Assumptions1. We are given the expression $-\frac{c}{5}+9 c^{3} d^{4}+c^{} d^{3}$ . . We need to determine if this expression is a polynomial or not.
3. If it is a polynomial, we need to state the type and degree of the polynomial.

STEP 2

A polynomial is an algebraic expression that can have one or more terms, but each term must be a product of a constant and a variable raised to a non-negative integer exponent.

STEP 3

Let's examine each term of the given expression to see if it meets the criteria of a polynomial.
The first term is $-\frac{c}{5}$ , which is the product of a constant and a variable raised to the power of1. This term meets the criteria.

STEP 4

The second term is $9 c^{3} d^{4}$ , which is the product of a constant and variables raised to non-negative integer exponents. This term meets the criteria.

STEP 5

The third term is $c^{2} d^{3}$ , which is the product of a constant (in this case,1) and variables raised to non-negative integer exponents. This term meets the criteria.

STEP 6

Since all terms of the given expression meet the criteria of a polynomial, we can conclude that the expression $-\frac{c}{5}+9 c^{3} d^{4}+c^{2} d^{3}$ is a polynomial.

STEP 7

Now, we need to determine the type and degree of the polynomial. The type of a polynomial is determined by the number of terms it has. Our polynomial has three terms, so it is a trinomial.

STEP 8

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

STEP 9

The first term, $-\frac{c}{5}$ , has a total degree of.

STEP 10

The second term, $9 c^{3} d^{4}$ , has a total degree of $3+4=7$ .

STEP 11

The third term, $c^{} d^{3}$ , has a total degree of $+3=5$ .

STEP 12

The highest total degree among all terms is7, so the degree of the polynomial is7.
The given expression $-\frac{c}{5}+9 c^{} d^{4}+c^{2} d^{}$ is a trinomial of degree7.

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QuestionIs the expression −c5+9c3d4+c2d3-\frac{c}{5}+9 c^{3} d^{4}+c^{2} d^{3}−5c​+9c3d4+c2d3 a polynomial? If yes, identify its type and degree.

Studdy Solution

STEP 1

Assumptions1. We are given the expression −c5+9c3d4+cd3-\frac{c}{5}+9 c^{3} d^{4}+c^{} d^{3}−5c​+9c3d4+cd3. . We need to determine if this expression is a polynomial or not.3. If it is a polynomial, we need to state the type and degree of the polynomial.

STEP 2

A polynomial is an algebraic expression that can have one or more terms, but each term must be a product of a constant and a variable raised to a non-negative integer exponent.

STEP 3

Let's examine each term of the given expression to see if it meets the criteria of a polynomial.The first term is −c5-\frac{c}{5}−5c​, which is the product of a constant and a variable raised to the power of1. This term meets the criteria.

STEP 4

The second term is 9c3d49 c^{3} d^{4}9c3d4, which is the product of a constant and variables raised to non-negative integer exponents. This term meets the criteria.

STEP 5

The third term is c2d3c^{2} d^{3}c2d3, which is the product of a constant (in this case,1) and variables raised to non-negative integer exponents. This term meets the criteria.

STEP 6

Since all terms of the given expression meet the criteria of a polynomial, we can conclude that the expression −c5+9c3d4+c2d3-\frac{c}{5}+9 c^{3} d^{4}+c^{2} d^{3}−5c​+9c3d4+c2d3 is a polynomial.

STEP 7

Now, we need to determine the type and degree of the polynomial. The type of a polynomial is determined by the number of terms it has. Our polynomial has three terms, so it is a trinomial.

STEP 8

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

STEP 9

The first term, −c5-\frac{c}{5}−5c​, has a total degree of.

STEP 10

The second term, 9c3d49 c^{3} d^{4}9c3d4, has a total degree of 3+4=73+4=73+4=7.

STEP 11

The third term, cd3c^{} d^{3}cd3, has a total degree of +3=5+3=5+3=5.

STEP 12

The highest total degree among all terms is7, so the degree of the polynomial is7.The given expression −c5+9cd4+c2d-\frac{c}{5}+9 c^{} d^{4}+c^{2} d^{}−5c​+9cd4+c2d is a trinomial of degree7.

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QuestionIs the expression $-\frac{c}{5}+9 c^{3} d^{4}+c^{2} d^{3}$ a polynomial? If yes, identify its type and degree.

Assumptions1. We are given the expression $-\frac{c}{5}+9 c^{3} d^{4}+c^{} d^{3}$ . . We need to determine if this expression is a polynomial or not.
3. If it is a polynomial, we need to state the type and degree of the polynomial.

Let's examine each term of the given expression to see if it meets the criteria of a polynomial.
The first term is $-\frac{c}{5}$ , which is the product of a constant and a variable raised to the power of1. This term meets the criteria.

The second term is $9 c^{3} d^{4}$ , which is the product of a constant and variables raised to non-negative integer exponents. This term meets the criteria.

The third term is $c^{2} d^{3}$ , which is the product of a constant (in this case,1) and variables raised to non-negative integer exponents. This term meets the criteria.

Since all terms of the given expression meet the criteria of a polynomial, we can conclude that the expression $-\frac{c}{5}+9 c^{3} d^{4}+c^{2} d^{3}$ is a polynomial.

The first term, $-\frac{c}{5}$ , has a total degree of.

The second term, $9 c^{3} d^{4}$ , has a total degree of $3+4=7$ .

The third term, $c^{} d^{3}$ , has a total degree of $+3=5$ .

The highest total degree among all terms is7, so the degree of the polynomial is7.
The given expression $-\frac{c}{5}+9 c^{} d^{4}+c^{2} d^{}$ is a trinomial of degree7.