Question

List all the factors of the monomial.

$2r^{3}s$

Short answer

The list of the factor of the monomial is 1, 2, r, $r^2$, $r^3$, s, $rs$, $r^{2}s$, $r^{3}s$, $2r, 2r^2, 2r^3, 2s, 2rs, 2r^{2}s,$and $2r^{3}s$.

Step-by-step solution

  Define monomials

A monomial is an expression that has a single term, with variables and a coefficient. For example, $2xy$ is a monomial since it is a single term, has two variables, and one coefficient.

  State the concept to factor the monomial

To factor a monomial completely, write the coefficient as a product of primes and expand the variable part.

  Factor the monomial

First, expand and separate the variables from its coefficients.

$\text{2}|r^{3}s$

In the next step, expand each individually-

$2r^{3}s=2\times r\times r\times r\times s$

Therefore, the factors of the monomial $2r^{3}s$are 1, 2, r, $r^2$, $r^3$, s, $rs$, $r^{2}s$, $r^{3}s$, $2r, 2r^2, 2r^3, 2s, 2rs, 2r^{2}s,$and $2r^{3}s$.