Transcript Factoring out the GCF
Meet Gi Na. She loves to play her flute outside in the fresh air, close to nature. Gi Na's friend, Chaika, loves to do Ollies on her skateboard at the city skate park. Whoa, look at her go! This is Fernando. He likes to hang out in his room with his Chameleon, Oscar. These three friends have three VERY different interests.
GCF in everyday life
But, Gi Na likes to do lots of other things too. She likes crossword puzzles, glass blowing, painting, origami, karaoke, jewelry making, doityourself projects, Sudoku, sewing, knitting. It’s a long list, you get the picture. In addition to skateboarding, Chaika likes photography, music, snowboarding, snake boarding, watching movies and tv, metal working, graffiti, hip hop and karaoke. Another long list of interests.
Fernando also likes drawing, acting, doing Sudoku puzzles, collecting insects, roasting coffee, arranging flowers, singing Karaoke, cheerleading, and making movies. The three friends want to do something together, but something they ALL enjoy, an interest that’s common to all three. How can we figure this out? It's like finding the Greatest Common Factor, or GCF for short.
The Greatest Common Factor in math
We can relate this real world problem to a math topic, finding the Greatest Common Factor. To make polynomials easier to work with, we factor out the Greatest Common Factor and to do this, we undo the Distributive Property. You can also think of it as the reverse of the Distributive Property.
First example
Let’s take a look at an example. 4x + 28. 4 is common to both terms, so by undoing or reversing the Distributive Property, we factor out the 4. Notice how I write this down, outside parentheses is the GCF, and inside parentheses is what's left of the expression after dividing all terms by the GCF.
Second example
Let’s try a second example, 4x² + 28x. You can write this as (4)(x)(x) + (4)(7)(x) Hmm, both terms have a common factor of 4 and they both have an 'x' so we can factor out 4 and also an 'x' and in a reverse of the Distributive Property, we display the GCF, 4x, outside the parentheses and what's left of the expression inside by dividing all terms by the GCF.
Last check
Don't forget: to check your work, you can apply the Distributive Property. Looking good! Sometimes math teachers like to assign problems that look impossible to solve, but if you know the right steps, they're not that bad. Let’s try one of those now.
Oh boy, it’s a doozey, 10x³y² + 18x²y  4x. (2 * 5) (x * x * x) (y * y) + (2 * 3 * 3) (x * x) * y  (2 * 2) (x) 2x is the GCF. So let's factor it out. Okay, what's the result 2x times the trinomial 5x²y² + 9xy + 2. Wow, that was a lot of work! Do you need to completely factor every term, everytime? No, probably most of the time, you can figure it out without writing out all the factors.
Summary
Okay, let's summarize. To find the Greatest Common Factor of a polynomial, find the factors common to each term in the polynomial. Back to our three friends. Did they figure out something they all like to do? Li Na and Leon like Sudoko, but Ayumi is not a fan, so that's not the GCF or the common interest for all three. But… they all like Karaoke! It’s their GCF! But sadly, their taste in music is not a GCF.

Introduction to Polynomials – Naming Polynomials by Number of Terms

Adding Polynomials

Multiplying Polynomials

Multiplying Special Case Polynomials

Factoring out the GCF

Factoring Trinomials with a = 1

Factoring Trinomials with a ≠ 1

Factoring Special Case Polynomials

Factoring by Grouping

Subtracting Polynomials