Question

List all the factors of the monomial.

$6a{b}^2$

Short answer

The list of the factor of the monomial is 1, 2, 3, 6, a, b, $b^2$, $ab$, $a{b}^2$, $2a, 2b, 2b^2, 2ab, 2a{b}^2$, $3a, 3b, 3b^2, 3ab, 3a{b}^2$, $6a, 6b, 6b^2, 6ab$ and $6a{b}^2$.

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.

$\text{6}|{\text{ab}}^2$

In the next step, expand each individually-

$6a{b}^2=2\times 3\times a\times b\times b$

Therefore, the factors of the monomial $6a{b}^2$are 1, 2, 3, 6, a, b, $b^2$, $ab$, $a{b}^2$, $2a, 2b, 2b^2, 2ab, 2a{b}^2$, $3a, 3b, 3b^2, 3ab, 3a{b}^2$, $6a, 6b, 6b^2, 6ab$and $6a{b}^2$.