Hello amazing math people. We're going to look at common factors. If we have multiple terms in a polynomial, what we're going to do when we look for a common factor is we're going to think about what comes out of all of the terms. So in the first example, 2X to the 4th minus four X ^3 + 6 X. That all has a two and an X that could come out. If I divided a 2X out of two X to the 4th, that would leave me X ^3. If I divided a 2X out of -4 X cubed, that would give me a -2 X squared, and if I took a 2X out of 6X, that would give me a three. Sometimes I recommend to people who might struggle with this to actually think about writing each term over the common factor and then simplifying it down. Some people find that much easier to see. So that the twos here would cancel X to the 4th over X leaves me that X ^3 2 goes into four twice, X ^3 / X is that X ^2 2 goes into six three times and those XS would cancel. Sometimes we have polynomials that can only have a coefficient come out. So in this case we could take out a three and we'd get X + 2 left. Want to emphasize, we could also technically take out a -3 and we'd get negative X -, 2. Sometimes it's important to be able to take out a negative. We also might have nothing in common, and if there's nothing in common, we can always take out A1. If there's nothing other than A1 in common, the polynomial is called prime. The polynomial is called prime. Now, sometimes we have lots of terms like a * B + C + D * B + C When we look at this, it might appear that nothing is in common. There's actually two terms here. A * b + C is all one term and D * b + C is all one term. Because terms are separated by pluses and minuses, and this a is being multiplied by that whole parenthesis, the D is being multiplied. So when I look at these two terms, do they have anything in common? And the answer is yes, they both have AB plus C If I take out the B + C, if I take out what's in common, what does that leave us? That would leave us just an A in the first term and AD in the second term. So using the little trick I showed back a moment ago, if we thought of this AB plus C divided by the B + C, and we took the D and divided it by the B + C because that's what they have in common, is the B + C correct? Then those B plus CS are going to cancel, leaving the A + D for that other term. Now, we might also have just four terms, given AB plus CB plus AE plus CE. In this case, we're going to do what's called factoring by grouping. When we have 4 terms, we're going to usually start by grouping them two and two. Now this won't always work, but it frequently does. When we look at these first two, they have AB in common, leaving us A + C. When we look at the 2nd 2:00, they have an E in common, leaving us an A + C. So we had four terms that have now turned into two terms. And the question is, do these two terms have anything in common? And the answer is yes, they each have an A + C. So if I pull out an A + C, that leaves me B + E and that's a single term. And our goal whenever we're factoring is to get things down to a single term. Thank you and have a great day.