Factoring Monomials

Did you know that it's possible to break down a monomial into its prime factors the same way you can break down any whole number into its prime factors? It is, and in this article, we'll look at how.

The Fundamental Theorem of Arithmetic

The Fundamental Theorem of Arithmetic states that every integer greater than 1 is either a prime number or can be expressed in the form of primes. Basically, all of the natural numbers can be expressed in the form of the product of their prime factors. Remember that a prime number is a number that is divisible by 1 and itself only.

An example of a prime number is 13. It can only be divided by 1 and itself.

The number 26, on the other hand, is not a prime number. It can be factorized into its primes:

$13*2=26$

The prime factorization of monomials

The prime factorization of a monomial is an expression of its prime numbers, single variables, and possibly a -1.

Example 1

Find the prime factorization of the monomial $-45x^{3}y{z}^5$ .

First, find the prime factors for 45. Start with $5*9$ . Then 9 can be broken down further into $3*3$ , making $3*3*5$ the prime factorization of 45.

Then write the powers out individually and add a -1 to the beginning to make the whole thing negative.

$-1*3*3*5*x*x*x*y*z*z*z*z*z$

Example 2

Find the prime factorization for the monomial $32p{q}^3{r}^2$ .

First, find the prime factors for 32. Start with $2*16$ . That breaks down to $2*2*8$ . That breaks down to $2*2*2*4$ . That breaks down to $2*2*2*2*2$ , and that's the prime factorization for 32.

Then write out the powers individually, and this time, there is no need to add a -1 because the monomial is not a negative monomial.

$2*2*2*2*2*p*q*q*q*r*r$

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Get help learning about factoring monomials

Tutoring is an excellent way for your student to come to a thorough understanding of factoring monomials. If your student isn't fully understanding their classroom teaching, supplement it with the help of a 1-on-1 private tutor. The tutor can determine exactly what is blocking your student from understanding the process and help them overcome the block until they grasp the concepts involved. A tutor can also help your student understand the ways they learn best and the strategies they can use based on that. These learning strategies will help your student learn to factor monomials and they can carry the skills to other math classes and even other subjects in school. To get your student set up with a suitable tutor, contact one of the helpful Educational Directors at Varsity Tutors today. We look forward to working with you.