Determine whether the following algebraic expression is a polynomial. Answer Yes or No. If it is a polynomial, state the degree and then state whether it is a monomial, a binomial, or a trinomial: 6 x 2 y 4 − 8 x 5 + 3.

Question

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Answer 1

Textbook Question

Chapter 5, Problem 1PCT

Determine whether the following algebraic expression is a polynomial. Answer Yes or No. If it is a polynomial, state the degree and then state whether it is a monomial, a binomial, or a trinomial: 6x²y⁴ − 8x⁵ + 3.

Expert Solution & Answer

To determine

Whether the expression 6x2y4−8x5+3 is a polynomial or not and find the degree.

Answer to Problem 1PCT

Yes, the given expression is a trinomial of degree 6.

Explanation of Solution

Definition used:

“A monomial or sum of monomials is known as a polynomial. The degree of a polynomial is the largest degree of all the terms in that polynomial”.

Observation:

The given expression is 6x2y4−8x5+3.

Observe that each term is either a number, a product of a number and a variable, a product of two variables or a variable alone, where all exponents are non-negative numbers.

Thus, the given expression is a sum of three monomials.

Hence, the given expression is a polynomial.

The degrees of the terms in the expression are as follows, {6, 5, 0}. The maximum of the degrees is 6.

Thus, the degree of the given polynomial is 6.

Thus, the given expression is a trinomial with degree 6.

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Answer 2

Textbook Question

Chapter 5, Problem 1PCT

Determine whether the following algebraic expression is a polynomial. Answer Yes or No. If it is a polynomial, state the degree and then state whether it is a monomial, a binomial, or a trinomial: 6x²y⁴ − 8x⁵ + 3.

Expert Solution & Answer

To determine

Whether the expression 6x2y4−8x5+3 is a polynomial or not and find the degree.

Answer to Problem 1PCT

Yes, the given expression is a trinomial of degree 6.

Explanation of Solution

Definition used:

“A monomial or sum of monomials is known as a polynomial. The degree of a polynomial is the largest degree of all the terms in that polynomial”.

Observation:

The given expression is 6x2y4−8x5+3.

Observe that each term is either a number, a product of a number and a variable, a product of two variables or a variable alone, where all exponents are non-negative numbers.

Thus, the given expression is a sum of three monomials.

Hence, the given expression is a polynomial.

The degrees of the terms in the expression are as follows, {6, 5, 0}. The maximum of the degrees is 6.

Thus, the degree of the given polynomial is 6.

Thus, the given expression is a trinomial with degree 6.

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Answer 3

Textbook Question

Chapter 5, Problem 1PCT

Determine whether the following algebraic expression is a polynomial. Answer Yes or No. If it is a polynomial, state the degree and then state whether it is a monomial, a binomial, or a trinomial: 6x²y⁴ − 8x⁵ + 3.

Expert Solution & Answer

To determine

Whether the expression 6x2y4−8x5+3 is a polynomial or not and find the degree.

Answer to Problem 1PCT

Yes, the given expression is a trinomial of degree 6.

Explanation of Solution

Definition used:

“A monomial or sum of monomials is known as a polynomial. The degree of a polynomial is the largest degree of all the terms in that polynomial”.

Observation:

The given expression is 6x2y4−8x5+3.

Observe that each term is either a number, a product of a number and a variable, a product of two variables or a variable alone, where all exponents are non-negative numbers.

Thus, the given expression is a sum of three monomials.

Hence, the given expression is a polynomial.

The degrees of the terms in the expression are as follows, {6, 5, 0}. The maximum of the degrees is 6.

Thus, the degree of the given polynomial is 6.

Thus, the given expression is a trinomial with degree 6.

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Answer 4

Textbook Question

Chapter 5, Problem 1PCT

Determine whether the following algebraic expression is a polynomial. Answer Yes or No. If it is a polynomial, state the degree and then state whether it is a monomial, a binomial, or a trinomial: 6x²y⁴ − 8x⁵ + 3.

Expert Solution & Answer

To determine

Whether the expression 6x2y4−8x5+3 is a polynomial or not and find the degree.

Answer to Problem 1PCT

Yes, the given expression is a trinomial of degree 6.

Explanation of Solution

Definition used:

“A monomial or sum of monomials is known as a polynomial. The degree of a polynomial is the largest degree of all the terms in that polynomial”.

Observation:

The given expression is 6x2y4−8x5+3.

Observe that each term is either a number, a product of a number and a variable, a product of two variables or a variable alone, where all exponents are non-negative numbers.

Thus, the given expression is a sum of three monomials.

Hence, the given expression is a polynomial.

The degrees of the terms in the expression are as follows, {6, 5, 0}. The maximum of the degrees is 6.

Thus, the degree of the given polynomial is 6.

Thus, the given expression is a trinomial with degree 6.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

Whether the expression 6x2y4−8x5+3 is a polynomial or not and find the degree.

Answer to Problem 1PCT

Yes, the given expression is a trinomial of degree 6.

Explanation of Solution

Definition used:

“A monomial or sum of monomials is known as a polynomial. The degree of a polynomial is the largest degree of all the terms in that polynomial”.

Observation:

The given expression is 6x2y4−8x5+3.

Observe that each term is either a number, a product of a number and a variable, a product of two variables or a variable alone, where all exponents are non-negative numbers.

Thus, the given expression is a sum of three monomials.

Hence, the given expression is a polynomial.

The degrees of the terms in the expression are as follows, {6, 5, 0}. The maximum of the degrees is 6.

Thus, the degree of the given polynomial is 6.

Thus, the given expression is a trinomial with degree 6.

Answer 8

Expert Solution & Answer

To determine

Whether the expression 6x2y4−8x5+3 is a polynomial or not and find the degree.

Answer to Problem 1PCT

Yes, the given expression is a trinomial of degree 6.

Explanation of Solution

Definition used:

“A monomial or sum of monomials is known as a polynomial. The degree of a polynomial is the largest degree of all the terms in that polynomial”.

Observation:

The given expression is 6x2y4−8x5+3.

Observe that each term is either a number, a product of a number and a variable, a product of two variables or a variable alone, where all exponents are non-negative numbers.

Thus, the given expression is a sum of three monomials.

Hence, the given expression is a polynomial.

The degrees of the terms in the expression are as follows, {6, 5, 0}. The maximum of the degrees is 6.

Thus, the degree of the given polynomial is 6.

Thus, the given expression is a trinomial with degree 6.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

Whether the expression 6x2y4−8x5+3 is a polynomial or not and find the degree.

Answer 12

Answer to Problem 1PCT

Yes, the given expression is a trinomial of degree 6.

Answer 13

Explanation of Solution

Definition used:

“A monomial or sum of monomials is known as a polynomial. The degree of a polynomial is the largest degree of all the terms in that polynomial”.

Observation:

The given expression is 6x2y4−8x5+3.

Observe that each term is either a number, a product of a number and a variable, a product of two variables or a variable alone, where all exponents are non-negative numbers.

Thus, the given expression is a sum of three monomials.

Hence, the given expression is a polynomial.

The degrees of the terms in the expression are as follows, {6, 5, 0}. The maximum of the degrees is 6.

Thus, the degree of the given polynomial is 6.

Thus, the given expression is a trinomial with degree 6.