Chapter 6, Problem 588RE

In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.

588.

(a) $11c^4-23c^2+1$

(b) $9p^3+6p^2-p-5$

(c) $\frac{3}{7}x+\frac{5}{14}$

(d) $10$

(e) $2y-12$

To determine

(a)

To decide if the given polynomial is a monomial, binomial, trinomial or other polynomial.

Answer to Problem 588RE

Trinomial.

Explanation of Solution

Given information:

A polynomial is given as $11c^4-23c^2+1$.

Calculation:

As we know that, a term is a constant or the product of a constant and one or more variables. An algebraic term in the form of $a{x}^m$ where $a$ is the constant and $m$ is a whole number is called a monomial.

A monomial, or two or more monomials combined by addition or subtraction, is calleda polynomial.

If a polynomial have only one term then it is called a monomial.

If a polynomial have exactly two term then it is called a binomial.

If a polynomial have three term then it is called a trinomial.

Polynomial with more than three terms are just called polynomial.

We have been given a polynomial as $11c^4-23c^2+1$.

Since, given polynomial has three terms.

Therefore, we can say that given polynomial is trinomial.

To determine

(b)

To decide if the given polynomial is a monomial, binomial, trinomial or other polynomial.

Answer to Problem 588RE

Polynomial.

Explanation of Solution

Given information:

A polynomial is given as $9p^3+6p^2-p-5$.

Calculation:

As we know that, a term is a constant or the product of a constant and one or more variables. An algebraic term in the form of $a{x}^m$ where $a$ is the constant and $m$ is a whole number is called a monomial.

A monomial, or two or more monomials combined by addition or subtraction, is calleda polynomial.

If a polynomial have only one term then it is called a monomial.

If a polynomial have exactly two term then it is called a binomial.

If a polynomial have three term then it is called a trinomial.

Polynomial with more than three terms are just called polynomial.

We have been given a polynomial as $9p^3+6p^2-p-5$.

Since, given polynomial has more than three terms.

Therefore, we can say that given polynomial is other polynomial.

To determine

(c)

To decide if the given polynomial is a monomial, binomial, trinomial or other polynomial.

Answer to Problem 588RE

Binomial.

Explanation of Solution

Given information:

A polynomial is given as $11c^4-23c^2+1$.

Calculation:

As we know that, a term is a constant or the product of a constant and one or more variables. An algebraic term in the form of $a{x}^m$ where $a$ is the constant and $m$ is a whole number is called a monomial.

A monomial, or two or more monomials combined by addition or subtraction, is calleda polynomial.

If a polynomial have only one term then it is called a monomial.

If a polynomial have exactly two term then it is called a binomial.

If a polynomial have three term then it is called a trinomial.

Polynomial with more than three terms are just called polynomial.

We have been given a polynomial as $\frac{3}{7}x+\frac{5}{14}$.

Since, given polynomial has two terms.

Therefore, we can say that given polynomial is binomial.

To determine

(d)

To decide if the given polynomial is a monomial, binomial, trinomial or other polynomial.

Answer to Problem 588RE

Monomial.

Explanation of Solution

Given information:

A polynomial is given as $10$.

Calculation:

As we know that, a term is a constant or the product of a constant and one or more variables. An algebraic term in the form of $a{x}^m$ where $a$ is the constant and $m$ is a whole number is called a monomial.

A monomial, or two or more monomials combined by addition or subtraction, is calleda polynomial.

If a polynomial have only one term then it is called a monomial.

If a polynomial have exactly two term then it is called a binomial.

If a polynomial have three term then it is called a trinomial.

Polynomial with more than three terms are just called polynomial.

We have been given a polynomial as $10$.

Since, given polynomial has only one term.

Therefore, we can say that given polynomial is monomial.

To determine

(e)

To decide if the given polynomial is a monomial, binomial, trinomial or other polynomial.

Answer to Problem 588RE

Binomial.

Explanation of Solution

Given information:

A polynomial is given as $2y-12$.

Calculation:

As we know that, a term is a constant or the product of a constant and one or more variables. An algebraic term in the form of $a{x}^m$ where $a$ is the constant and $m$ is a whole number is called a monomial.

A monomial, or two or more monomials combined by addition or subtraction, is calleda polynomial.

If a polynomial have only one term then it is called a monomial.

If a polynomial have exactly two term then it is called a binomial.

If a polynomial have three term then it is called a trinomial.

Polynomial with more than three terms are just called polynomial.

We have been given a polynomial as $2y-12$.

Since, given polynomial has two terms.

Therefore, we can say that given polynomial is binomial.