It is no secret that factoring is one the biggest and central units in all of Algebra, but I find it to be one of the most exciting topics we get to explore.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
The cornerstone for factoring polynomials is learning how we factor integers!
And this is where our incredible journey will begin.
First, let’s start with remembering what a Prime Number is…
.. a prime is an integer greater than one that has no positive factors other than one and itself.
So when we are asked to factor a number, we are looking to write it as a product of prime-number factors.
This is called Prime Factorization or factoring integers into primes.
Prime Factorization Example
But the coolest thing about factoring over the integers is that we don’t have to be so elaborate as to reducing each number to its base prime values.
Instead, we just need to list all the groups of numbers whose product equals the original number, as SOS Math so nicely states.
We will quickly see that our ability to find all the multiples of a number is going to be the key to handling the most important factoring principal…
… the Greatest Common Factor (GCF)!
What is the GCF, you may ask?
It is the greatest number, or monomial that all terms have in common. In other words, what’s the biggest thing they share?
We are going to not only find the Integer factorization for given numbers, utilizing a neat “factor tree” technique, but we are going to learn how to list pairs of integral factors to determine the GCF for various numbers.
In other words, we’re going to become pros at factoring over the integers!
Prime Factorization (How-To) – Video
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