Factoring by Grouping - Factoring Polynomials

hi guys it's me teacher going in today's video we will talk about factoring by grouping and we have here an example of it and later on we will solve for this example together with two more examples so that further ado let's do this topic so i have here this first two examples on how do we perform factoring by grouping so we have here x cubed minus two x squared plus five x minus ten so how do we do how do we perform factoring by grouping as you can see we are on time four different terms one two three and four normally if maritime four terms we will regroup them into two different groups so in this case we will enclose them by parentheses by terms so many more times partner in new terms factor but in this case and intuico we have your x cubed minus 2x square then enclose it by parenthesis and this one plus enclose 5x minus 10 by the parentheses we have here 5x minus 10. now since we are done regrouping them we need to think of their common monomial factor here in x cubed minus 2x squared the common monomial factor is x squared so we will put it outside the parenthesis now we will make a parenthesis and to get the factor inside this parenthesis we will simply divide these terms using our common monomial factor which is x squared so x cubed divided by x squared the answer is x and for this term divided by x square the answer is minus two next put a plus here and as you can see between 5x minus 10 the common monomial factor is 5. so we will prepare a parenthesis here and to get the factor inside this parenthesis simply divide these two terms by five five x divided by five is simply x the negative ten divided by five is minus two so i will use orange marker x negative 10 divided by 5 s minus 2 and as you can see upon factoring using common minor factoring and here it is maritime common common factor which is x minus 2 and x minus 2. so we will copy this one we have x minus 2 and then after removing x minus 2 as you can see what will remain is x squared plus 5 and we will put that x square plus 5 inside the parenthesis so it is x square plus five and as you can see we already factored the given polynomial x cubed minus two x squared plus five x minus ten belong x minus two times x squared plus five and these are the factors okay now let's continue with item number two for item number two we are given three x cubed plus two x square plus six x plus four we will regroup them we will choose this two factor these two terms we have three x cubed plus two x square as your first group plus always additional plus the second group six x plus four the very reason behind human term stand because uh we can it's possible to for us to produce a common monomial factor here in this first group the common linear factor is again x square then parenthesis to find the terms inside the parenthesis divide this by x square and divide this by x square so as you can see one dividing three x cubed divided by x squared that is three x then two x squared divided by x squared is plus two and these are the factors of three x cubed plus two x square next here the common molar factor 6x plus 4 is simply 2. prepare parenthesis and divide each term by 2. so divided by 2 and divided by 2. and as you can see 6x divided by 2 is simply 3x then 4 divided by 2 is plus 2. and same pattern what will what happened here in number one as you can see we have the common binomial factor which is three x plus two so we will put out we will get three x plus two and then as you can see upon removing three x plus two what remain is x squared plus two so the other factor is simply x squared plus two and these are the factors of the given polynomial 3x cubed plus 2x squared plus 6x plus 4. now let's move on with our last example for our last example as you can see we have here 3x plus 7y okay we will adjust the paper 3x 7y minus 21 minus xy so as you can see guys here if we will group 3x and 7y there is no common factor okay so there is no common factor so what we need to do is to pair this uh the following terms here is your first pair and this is your second pair so what will happen is that we will enclose them by using the parenthesis this first we have 3x minus xy so we choose 3x minus xy because obviously we the the common monomial factor is x then always plus then enclose the second group by the parenthesis we have 7y minus 21. now as you can see we need to factor it out the common millennial factor here is simply x so let's put x outside the parenthesis x then parenthesis so we will divide each term by x and each term by x 3x divided by x is simply three then what's next is that negative x y divided by x is minus y or the second group oh i use a different color let's get three in that opinion plus obviously your common millennial factor is seven so we have seven outside and then the parenthesis we will divide each term by seven to get the other factor seven okay seven is simply y negative 23 divided by 7 is negative 3. as you can see it looks like that these two factors are the same we have three y three minus y and y minus three so as you can see we can we can manipulate this as y minus 3 be equal to negative 3 plus y so what will happen to make this 3y minus y we will extract negative negative sign from 3 y and y 3 and y it will become 3 minus y upon checking negative times 3 is negative 3 negative times y negative y is positive y so what will happen here so we will multiply this negative to 7 it will become x times 3 minus y and this positive 7 will become negative 7 because we have here negative and we have three minus y so as you can see we have a common binomial factor and that is three minus y we will copy this as f as the first factor we have three minus y then upon removing this this will give you only x minus minus seven so we have x minus seven and these are the factors of your third polynomial so we hope you guys learned something from this video on how to factor polynomials using factoring by grouping so if you're new to my channel don't forget to like and subscribe but hit the link below again it's meeting shergon bye

Channel: MATH TEACHER GON

Views: 39,691

Keywords: factoring, factoring by grouping, factoring polynomials, polynomials, factoring techniques, difference of two squares, common monomial factoring, how to factor polynomials, how to do factoring by grouping, grade 8 math, grade 8, math, algebra, polynomial factoring, teacher gon

Id: C2uo545MyM4

Length: 10min 47sec (647 seconds)

Published: Wed Sep 14 2022