Guest Posted February 2, 2009 Report Share Posted February 2, 2009 Hey, We have recently started factoring Perfect Square Trinomials. I basicly need help converting the PST into the Square of a Sum/Diffrence. Here are a couple Problem from my HW. If someone could talk me through it, it would help ALOT Factor: y2 + 6y + 9 x2 - 4x + 4 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 2, 2009 Report Share Posted February 2, 2009 (edited) I believe I can help you with this. If you only need help with factoring perfect square trinomials, it's really simple. The trick is this: Say you have an expression: x2 + ax + (a/2)2 where a is an integer(it doesn't have to be an integer, it's just simpler that way). The factored form is simply: (x + a/2)2 The logic behind it is simple, if you multiply it out, you get: (x + a/2)(x + a/2) = x2 + ax/2 + ax/2 + a2 = x2 + ax + (a/2)2 Which is what we started with. I can give you a more general factoring pattern if you need it. Hope that helps. Edit: Added better explanation Edited February 2, 2009 by Frost Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 2, 2009 Report Share Posted February 2, 2009 (edited) I believe I can help you with this. If you only need help with factoring perfect square trinomials, it's really simple. The trick is this: Say you have an expression: x2 + ax + (a/2)^2 where a is an integer(it doesn't have to be an integer, it's just simpler that way). The factored form is simply: (x + a/2)2 The logic behind it is simple, if you multiply it out, you get: (x + a/2)(x + a/2) = x^2 + ax/2 + ax/2 + a^2 = x2 + ax + (a/2)^2 I can give you a more general factoring pattern if you need it. So based on this, y2 + 6y + 9 = (y+3)2? and for the other one the answer would be (x-2)2? If that is the correct answer then thank you very much! Edited February 2, 2009 by O'mally Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 2, 2009 Report Share Posted February 2, 2009 Yep, those are correct. It never hurts to check by multiplying them back out. Quote Link to comment Share on other sites More sharing options...
0 Izzy Posted February 2, 2009 Report Share Posted February 2, 2009 You're getting to the fun part of a book when it actually helps to pay attention. Quadratic equation coming up in a few lessons. (It's fun, and a helluva lot easier than FOILing.) Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 2, 2009 Report Share Posted February 2, 2009 Hey, We have recently started factoring Perfect Square Trinomials. I basicly need help converting the PST into the Square of a Sum/Diffrence. Here are a couple Problem from my HW. If someone could talk me through it, it would help ALOT Factor: y2 + 6y + 9 x2 - 4x + 4 Well, Frost did an amazing job explaining it, but I just want to add: Doing questions like these, all you have to remember is find 2 numbers that multiply to the last number (9 in the first equation) and add to the middle number (6 in the first equation), although you probably already knew that. When doing perfect squares, all you really have to do is either divide the middle number by 2 (6/2=3) or square rooting the last number (3*3=9), and inserting it in the equation (x +/- n), where n is the number you get. n is positive when the middle term is positive, negative when the middle term is negative. Oh boy, I think I just confused you more... Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 2, 2009 Report Share Posted February 2, 2009 I find that FOIL is a lot easier that the Quadratic formula and also gets used a LOT more. Also, math textbooks generally don't explain anything. They give an example and expect you to understand how they did it. (at least, the only math textbooks I ever saw did that) Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 2, 2009 Report Share Posted February 2, 2009 Having been through a bit of math, I almost never use FOIL (though I admit it's come in handy in a few key situations, particularly when reverse engineering a formula I was supposed to already know...) and the quadratic formula is EVERYWHERE. Learn them both, but trig is like the foundation of college math (upon which a very dark and dreary home was built) Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 2, 2009 Report Share Posted February 2, 2009 Having been through a bit of math, I almost never use FOIL (though I admit it's come in handy in a few key situations, particularly when reverse engineering a formula I was supposed to already know...) and the quadratic formula is EVERYWHERE. Learn them both, but trig is like the foundation of college math (upon which a very dark and dreary home was built) Ooh, thanks for the reassurance I actually never learnt FOIL, and had never even heard of such thing until after I already learnt how to do it Personally, I find Quadratic stuff fun, but maybe it's just me Quote Link to comment Share on other sites More sharing options...
0 unreality Posted February 2, 2009 Report Share Posted February 2, 2009 i hate FOIL... I never use any of those methods (FOILing, synthetic, completing the square, quadratic formula, etc), I just do it in my head ~ unless I absolutely can't figure it out, then I use the quadratic Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 2, 2009 Report Share Posted February 2, 2009 Well, FOILing works out well, if you need to do it in your head, try using (x-y)(x-y) Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 3, 2009 Report Share Posted February 3, 2009 Lol, Izzy, your prediction came true. Today we started factoring Qudratic Trinomials. Not fun. Thank you for all the help though Quote Link to comment Share on other sites More sharing options...
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Guest
Hey, We have recently started factoring Perfect Square Trinomials.
I basicly need help converting the PST into the Square of a Sum/Diffrence.
Here are a couple Problem from my HW. If someone could talk me through it, it would help ALOT
Factor:
y2 + 6y + 9
x2 - 4x + 4
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