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Algebra and Applications P. Pathak Worksheet 3 Section 5. 3 Factoring Trinomials of the form ax2 bx c Factor completely. 1. 2x2 5x 3 27. 22x2 29x 6 2. 2x2 5x 2 28. 20z 2 7z 6 3. 2y 2 13y 20 29. 2x2 1xy 10y 2 4. 2y 2 11y 15 30. 2x2 11xy 12y 2 5. 2t2 7t 15 31. 3x2 28xy 32y 2 6. 2t2 9t 35 7. 2x2 3x 20 33. 5x2 27xy 10y 2 8. 2x2 11x 21 34. 5x2 6xy 8y 2 9. 3y 2 13y 10 35. 7x2 10xy 3y 2 10. 3x2 17x 20 36. 6x2 7xy 3y 2 11. 3y 2 17y 28 37. 2x3 5x2 12x 12. 3y 2 13y 14 38. 3x3 19x2...
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In this video we're going to focus on factoring trinomials particularly in the form ax squared plus BX plus C where the leading coefficient is not 1 so we're going to go over some easy examples at first and then towards the end of the video we're going to go over a few harder examples when you have to deal with large numbers particularly when C is very large so let's begin let's start with 2x squared minus 5x minus 3 so if you know how to factor this feel free to pause the video and try it yourself now the first thing we're going to do is multiply the first number and the last number so 2 times negative 3 is negative 6 now you want to find two numbers that multiply to negative 6 but add to negative 5 so it can't be 2 and negative 3 because if you add them you get negative 1 but it's going to have to be negative 6 and 1 negative 6 times 1 is negative 6 but negative 6 plus 1 is negative 5 so what we're going to do is we're going to replace the middle term the negative 5 X with negative 6 X + 1 X negative 6 X + 1 X is negative 5 X and so we haven't changed the value of this expression at this point so we need to factor by grouping at this point in the first two terms what can we take out what's the GCF the greatest common factor the greatest common factor is 2x so 2x squared and divided by 2x that is going to equal X and negative 6x divided by 2x that's negative 3x or no that's actually just negative 3 I'll take that back all we could do at this point for the last two is take out a 1 because there is no GCF and so we're just going to have X minus 3 on the inside if these two are the same then your honor by track so let's factor out X minus 3 now what's going to be in the next parentheses it's going to be what's on the outside 2x and the 1 so it's going to be 2x plus 1 and so that's how you can factor a trinomial whenever the leading coefficient is not 1 so let's try another one 6x squared plus 13x minus 5 so let's multiply 6 by negative 5 for the first and the last two numbers 6 times negative 5 is negative 30 now what two numbers multiply to negative 30 but add to 13 well let's make a list if we divide negative 30 by 1 we're going to get negative 30 if we divided by 2 we'll get negative 15 if we divided by 3 we'll get negative 10 for does it go into it but if we divided by 5 we'll get negative 6 notice that 2 and 15 they differ by 13 2 plus negative 15 is negative 13 so if we make it negative 2 1 plus 15 it works negative 2 times positive 15 is negative 30 but negative 2 plus 15 that's positive 13 so let's replace the middle term with negative 2 X plus 15 X the order in which you write it doesn't matter it's going to work out the same way now in the next step we're going to factor by grouping so in the first two terms let's take out the GCF which is 2x so 6x squared divided by 2x is 3x and negative 2x divided by 2x that's negative 1 now what's the GCF between the last two terms between 15 X and negative 5 this is going to be positive 5 if we take...