hi guys it's me teacher going in today's video we will talk about common monomial factoring here in the philippines this topic is andrograde in mathematics so without further ado let's do this topic so the key thing here is first you need to find the right value or the right gcf or the greatest common factor in each term or in this given expression in number one we have six x y cubed plus 24 x squared y so first thing you need to do here is to identify what is the gcf between the coefficients 6 and 24. as you can see their greatest common factor or the gcf is equal to 6. and for the variables domain you will compare first the variable x x and x squared you will go with the variable with the least exponent here the gcf of x and x squared we have the variable x and as for the y variable let us compare y cube and y so we will go with y because it has of exponents right now you have the gcf of 6xy so what you need to do to find the other factor is that you will divide each term 6xy cube [Music] and 24 x squared y by your greatest common factor 6xy remember this is your gcf so we will copy six x y cubed divided by your gcf 6 x and y as you can see you can eliminate 6 and 6 as well as your x and x for the y variable you have y cubed divided by y that would give you the answer of y squared that's why the other factor is y squared that is the first term and to get the second term you have to divide 24 x squared y again by your greatest common factor six x y you will divide 24 by six and that is equal to four and for the x variable as you can see we have x squared over x that is equal to x and then for the y variable we can cancel out y that's why the the quotient of 24x squared y and 6xy is 4x so this is now the second term of the factor and as you can see we are done factoring item number one etogen after getting the gcf 6xy you need to prepare another parenthesis or a parenthesis where in this will serve as your other factor and expect neo na the long term cn it will open parenthesis because in the given expression you only have two terms and this is now the factors of item number one by the way guys if you want to check your answer you can multiply this using the safety property at capacitor numbers automatic your factors are correct so let's move on with item number two for number two you will go first with 36 and negative 63 what is their gcf 36 and 63 their gcf is equal to 9. and for the variables you have x cubed and x to the fifth power you will go with x cubed because it has the least value of exponent for the y domain you have y raised to six y is seven you will go here with the y with the least exponent which is y raised to 6. prepare parenthesis and then you're expecting two terms because you have one and two terms so let's try divide this 36 x cubed y raised to 6 by your gcf 9x cubed y raised to 6. as you can see 36 divided by 9 is equal to 4 and for the x variable we can cancel up this out cancel this out cancel this out cancel this out and what will remain is equal to four the first term of the other factor is four and for the next term we have negative 63 x to the fifth power y raised to 7 divide this by your greatest common factor 9 x cubed y raised to 6. for negative 63 divided by 9 that would give you the answer of negative 7 okay we have negative 7. for the x variable you have x to the fifth power x cubed that is x squared copy your x then subtract five and three that is two for the y variable y raised to seven divided by y raised to six that is equal to y meaning the other fact or the second term of the other factor is negative seven or minus seven x squared and y and this is now the answer for item number two now let's move on with the third example that we have here and for example for the third example we are given 2x squared minus 4x cubed plus 18 x to the fifth power so we have 2 negative 4 and 18 definitely the gcf is 2. for the x variable you have x squared x cubed x to the fifth power you will go with x with the least exponent which is x squared so prepare parentheses and we are expecting three terms for the next factor because we have one two and three so let's start two x squared divided by two x squared as you can see they are the same that is equal to one so as easy as that so we have 1 then what we have here is negative 4 x cubed negative 4 x cubed divided by 2 x squared so negative 4 divided by 2 is simply negative 2. for the x variable we have x cubed over x squared that is equal to x meaning the second term here is minus or negative 2x copy this one 18 x to the fifth power divided by 2 x squared so 18 divided by 2 is equal to 9 x to the fifth power over x squared that is x cubed this is now the third term we have plus nine x cubed and close by parentheses and this is now the factors of item number three we have 2x squared times 1 minus 2x plus 9 x raised to the third power so i hope gaijin first and second entered that now let's move on with item number four for number four you have four x times x plus three minus one times x plus three as you can see guys here this is quite different or this is totally different from items number one two and three we're in we have we have two terms only here we have one and two pero factored for mimba term that in but don't worry as you can see marantine common which is x plus d and x plus 3 on the other side meaning to factor it out copy the common binomial which is x plus 3 and as you can see your first term here is 4x times x plus 3. since this is your gcf you will divide this by x plus 3. as you can see we can cancel this out cancel this out and what will remain is for x meaning you will you will prepare parenthesis which is 4x and here we have negative 1 or let's say negative 1 x plus 3 divide this by your common or your greatest common factor is x plus 3 cancel and cancel what really will remain is negative 1 or minus 1. and that's it guys this is now the factors of item number four so you guys i hope you learned something from this video so if you're new to my channel don't forget to like and subscribe but hitting the little bell button for you to be updated in latest uploads again it's me teacher going bye