Chapter 5, Problem 1RE

(a)

To determine

Whether $3x^2+9$ is a polynomial or not if yes, give the special name of the polynomial if it has one.

Answer to Problem 1RE

Solution:

Yes, the expression $3x^2+9$ is a polynomial and it is binomial.

Explanation of Solution

Given information:

Expression is $3x^2+9$.

A polynomial is a finite sum of monomial.

Now, while comparing expression $3x^2+9$ with the definition of a polynomial, it can be easily seen that this expression clearly follows all rules of a polynomial.

So, expression $3x^2+9$ is a polynomial.

As expression $3x^2+9$ has two terms, one is $3x^2$ and other is $9$. and a polynomial with two terms is classify as binomial polynomial. also, highest power of variable $x$ is $2$ here and polynomial in only single variable $x$, so it also can be referred as quadratic polynomial.

(b)

To determine

The polynomial $3x^2+9$ in descending order of the variable $x$.

Answer to Problem 1RE

Solution:

Descending order of the variable is $3x^2+9$.

Explanation of Solution

Given information:

Expression is $3x^2+9$.

To write a polynomial in descending order of its variable, the exponents on the variable descend or get lower as the terms go from left to right.

Here in expression $3x^2+9$ exponents of variable $x$ is already in descending order from left to right.

(c)

To determine

Degree of the polynomial $3x^2+9$.

Answer to Problem 1RE

Solution:

Degree of the polynomial expression $3x^2+9$ is $2$.

Explanation of Solution

Given information:

Expression is $3x^2+9$.

The degree of a term with whole number exponents is the highest sum of the exponents of the variables.

Here is expression $3x^2+9$ sum of exponents of the variable is $2$.

So, the degree of expression $3x^2+9$ is $2$.