[Music] in this video we will factor quadratic trinomials of the form x squared plus bx plus c also we will solve problems involving factors of polynomials all right let's start so first let us try to list all pairs of integers or factors of the following numbers so ibignatin lahatnam possible pairs of integers or factors numbers so first we have four so we have one and four or two and two okay and then six we have one and six two and three for eight we have one and eight two and four for ten we have one and ten two and five let's have another so we have twelve so we have one and twelve two and six three and four for eighteen we have one and eighteen two and nine three and six for twenty we have one and twenty two and ten four and five for thirty we have one and thirty 2 and 15 3 and 10 so these are just the x these are just examples okay [Music] in factoring general trinomials okay so a quadratic trinomial is just part of or an example of quadratic general trinomials okay so how to factor quadratic trinomial quadratic okay so since x squared plus b x plus c this is an example of quadratic trinomial so panu natin sha if a factor first we will list all pairs of integers whose product is c pairs of integers middle term which is your b okay so therefore the factored form of quadratic trinomial x squared plus b x plus c is equal to the product of x plus m and x plus n all right so liteco x squared plus b x plus c this is our factored form x plus m times x plus n where b is the sum and c is the product okay so you will think of two integers pairs of integers [Music] the resulting product must be c and this is our factored form let's have an example i have x squared plus 10 x plus 16. so in the given example first list all pairs of integers whose product is c all right so tatanda and bb gate item pairs of integers data type eating all right so we will have what are the factors of sixteen we have one and sixteen two and eight four and four okay so nistana integers pairs of integers next we will choose a pair whose sum is b so pili kadito nakapag inadmo so obviously it's two and eight okay so we will use two and eight so therefore this will serve as our m and n remember our factor is in the form of x plus m and times x plus n so therefore the factored form of x squared plus 10 x plus 16 is equal to the product of x plus two times x plus eight next so i have x squared minus nine x plus eighteen so again lista natin lahat will be positive now since negative middle term not n therefore the patient integer is nothing but a negative so we will have now negative 1 and negative 18 negative 2 and negative 9 negative 3 and negative 6. so all of these uh pairs of integers are all products factors of 18 okay so next we will choose a pair whose sum is b so that path negative nine so alindito ang negative nine kapaginat nathan so we have negative three and negative six and that is negative nine therefore our factored form is x uh from x squared minus nine x plus eighteen is x minus three and x minus six next i have x squared minus two x minus 24. so this is a different case okay so first list all the pairs of integers so again the total thing in since negative ito big sub pairs of integers so the larger integer must be negative integer you know positive not n s okay so therefore we have 1 and negative 24 2 and 12 negative 12 4 and negative 6 3 and negative 8. so all of these are factors of 24. now since negative nito and larger integer not in a negative so obviously you ate nothing you know negative young six nothing you know negative same as 12 and 24 all right so next we will choose a pair whose sum is b negative this one so we have 4 and negative 6 and that is equal to negative 2 so therefore our factored form of x squared minus 2x minus 24 is equal to the product of x plus 4 and x minus 6. next i have x squared plus 3x minus 10. so first step same procedure you have to list all the pairs of integers whose product is c okay larger integer so your smaller integer union negative all right so we have negative one and ten negative two and five so okay so next choose a pair whose sum is b so pd a positive three obviously it's negative 2 and 5 so that is 3. so therefore our factored form a of x squared plus 3x minus 10 is equal to x minus 2 and x plus five next i have x squared plus three x plus three so again list all the pairs of integers whose product is c so since so we have one and three now since one and three is equal to since we do not have a choice we only have these factors so one plus three is equal to four it doesn't satisfy the the quadratic trinomial so then x squared plus three x plus three cannot be factored using integer coefficients then it is an example of prime trinomials nothing prime trinomial because it cannot be factored next let us try to solve a problem so use factoring to find the dimensions of the given box with volume represented by the expression 4x cubed plus 16x squared minus 48x that the given expression or trinomial is not a quadratic trinomial why because the highest degree is three so alumni that the quadratic trinomial must be on the second degree so this is three so this is not a quadratic trinomial so first we will factor out for x so we will have four x times x squared plus four x minus twelve okay so etherness for x this will be the result all right so now we have now this quadratic trinomial so we can now factor okay so factor x squared plus 4x minus 12 so we will just copy for x and then x squared plus 4x minus 12. so again since negative toda but on the long integers nothing it's is some positive is a negative this is the resulting sum okay so 6 and negative 2 is equal to 4 6 times negative 2 that is negative 12 all right so therefore the dimension of the box are 4x x plus 6 and x minus 2. all right let's wrap up so again it's either both positive or both negative lanyan okay so pano natin malalaman next so since positive volt it's either both positive or both negative so since negative integers negative next i have uh minos a positive is a negative how and then the last case if this is negative again you must have one positive and one negative integer sodium hating and eviksabihen that your larger integer must be negative thank you for watching this video i hope you learned something don't forget to like subscribe and hit the bell button to our walmart channel just keep on watching