Chapter 6.8, Problem 2SGR

To determine

Whether the statement “Polynomials that cannot be factored are called $\text{Polynomials in one variable}$ .” is true or false.

Answer to Problem 2SGR

The statement “Polynomials that cannot be factored are called $\text{Polynomials in one variable}$ .” is false.

Explanation of Solution

Given information:

The statement “Polynomials that cannot be factored are called $\text{Polynomials in one variable}$ .”

Consider the provided statement “Polynomials that cannot be factored are called $\text{Polynomials in one variable}$ .”

The polynomials that cannot be factored are called $\text{Prime polynomials}$ .

The $\text{Polynomials in one variable}$are algebraic expressions that consist of terms In the form $a\times n$ where $n$ is a non-negative that means positive integer and $a$ is a real number.

A polynomial is in the form of: $4x{y}^2+3x-5$ .

The degree of a polynomial in one variable is the largest exponent in the polynomial.

For example: polynomial in one variable,

  $x^4-2x^2+x$

In this equation three terms are here but only one variable.

The example of Prime polynomial is:

  $x^2+3x+2$

This equation is not a prime polynomial as it can be written in the form of, $\left(x+1\right)\left(x+2\right)$ .

Thus, the statement “Polynomials that cannot be factored are called $\text{Polynomials in one variable}$ .” is false.