factoring quadratics: 3x^2 - x - 2, 400a^2 - 81b^2, etc
- Thread starter sarah.p
- Start date
There it is again. Do you live alone? Home Schooling still requires an instructor of some kind. Parent? Family Member? Itinerate Tutor? You simply can't have nothing.i cant see my instructor
i have to be home schooled
Please examine your resources realistically. You AND YOUR PARENTS need to have a chat with the local school district to see what other resources are available. If you "have to be home schooled", it is likely the school district is compelled to be of any necessary assistance.
Don't give up - with any excuse.
Don't beat yourself up - with any weapon.
Solve problems.
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Please don't use homeschooling as an excuse for not trying. Homeschoolers (like me) don't need that sort of advertising.sarah.p said:
To learn how to factor quadratics, please study on-topic lessons, such as:
. . . . .Factoring Quadratics
. . . . .Special Factoring
. . . . .WTANU: Factoring Trinomials
. . . . .Regents Prep: Factoring
. . . . .The Math Page: Factoring Trinomials
. . . . .MathGuide: Factoring Quadratic Trinomials
. . . . .WTAMU: Factoring Special Products
Once you have learned how to factor, please attempt these exercises. If you get stuck, please reply showing (with proper English) all the steps and reasoning you have tried.
Thank you.
Eliz.
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Whoever told you that was not telling the truth. There is no such classification. Just stop saying it.sarah.p said:
OK. Now, how about the rest? Where's the school district? There ARE solutions for people who try and work hard.sarah.p said:
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You are arguing, rather than listening. That is not helpful.sarah.p said:
No, it isn't. It is a geographical or political division that includes you. You are part of their responsibilities. You cannot do it all on your own. It is their responsibility to provide necessary resources. Do you live in Antartica? That could be tough. Maybe Sudan. OK, that could be a problem.
You're not stupid, you just need practice at factoring. It's everyone's bane
when they begin it. If you're like a lot of students, you'd rather pick
fly poop out of pepper with boxing gloves than factor, but still, you must
endeavor to perservere.
Here's a technique I often use for quadratics with leading coefficients
which aren't 1:
\(\displaystyle 3x^{2}-x-2\)
For #1, try to find two numbers which when multiplied equal -1(the
coefficient of x) and when added equal -6(3 times -2).
Let's see, -3 and 2. (-3)(2)=-6 and -3+2=-1
So, we have:
\(\displaystyle 3x^{2}-3x+2x-2\)
\(\displaystyle (3x^{2}-3x)+(2x-2)\)
Common factors:
\(\displaystyle 3x(x-1)+2(x-1)\)
The worst part is over. We now have it:
(3x+2)(x-1)
Try the same technique for #2. As for #3, take note, it's the difference of
2 squares. Visit the sites Stapel listed. They are very good and explain
well. Good luck and don't despair.
when they begin it. If you're like a lot of students, you'd rather pick
fly poop out of pepper with boxing gloves than factor, but still, you must
endeavor to perservere.
Here's a technique I often use for quadratics with leading coefficients
which aren't 1:
\(\displaystyle 3x^{2}-x-2\)
For #1, try to find two numbers which when multiplied equal -1(the
coefficient of x) and when added equal -6(3 times -2).
Let's see, -3 and 2. (-3)(2)=-6 and -3+2=-1
So, we have:
\(\displaystyle 3x^{2}-3x+2x-2\)
\(\displaystyle (3x^{2}-3x)+(2x-2)\)
Common factors:
\(\displaystyle 3x(x-1)+2(x-1)\)
The worst part is over. We now have it:
(3x+2)(x-1)
Try the same technique for #2. As for #3, take note, it's the difference of
2 squares. Visit the sites Stapel listed. They are very good and explain
well. Good luck and don't despair.
By far the simplest way of solving quadratic equations is by direct factoring. This does, however, depend on the ability to visualize the exact terms of the factors and definitely improves with experience. Take the following example for instance:sarah.p said:
1--Given x^2 + (6/3)x - (35/3) = 0
2--Multiplying through by 3 gives us 3x^2 + 16x - 35 = 0
3--We know that the factors take the form of (ax +/-b)x(cx +/-d)
4--Therefore, we must find values of a, b, c, and d that satisfy ax(x) = 3x^2, ax(+/-d) + cx(+/-b) = +16 and (+/-b)
(+/-d) = -35.
5--Clearly, ether a or c = 3 and b(d) = -5(7) or 5(-7)
6--A little mental arithmetic leads us to a = 3, b = -5, c = 1, and d = +7
7--This leaves us with (3x - 5)(x + 7) = 0
8--If either (3x - 5) or (x + 7) is zero, their product is zero
9--Therefore, 3x - 5 = 0 and x + 7 = 0 making x = +5/3 or -7.
YES Sarah!sarah.p said:
Next time, show stuff like a squared this way: a^2 (not a2).
Here's how you can prove you're correct:
multiply (20a - 9b) by 20a: 400a^2 - 180ab
multiply (20a - 9b) by 9b: 180ab - 81b^2
Add 'em up:
400a^2 - 180ab + 180ab - 81b^2
= 400a^2 - 81b^2 :idea:
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Really, I dare you to point out where you get the idea I am angry. It just isn't the case. My problem is trying to help someone who believes himself to be stupid and incapable. Why would anyone be able to help such an individual? You simply cannot get help as long as you hold that sort of thing in your mind. You came here to get help. Great. So far, I have seen everyone who has responded try to help you. Some have worked problems for you. Is that helping? Maybe. Some have taught brief lessons for you. Is that helping? Maybe. Some have tried to help you solve your attitude problems and feelings of hopelessness. Is that helping? Maybe. You are a whole person. You can't ignore an important piece of the learning puzzle. Your personal attitude will make it or break it. I know this is a math help site, but it will do no one any good to work a few algebra problems if you maintain that you simply cannot do it. If I'm angry, I will let you know. Now, let's learn some math.sarah.p said:If its thier responsibility than why are you angry at me? I was just trying to get help..
Can you name the organization that officially supplies the math teacher in Alberta? CIEE or something? It may be interesting to contact the organization and see exactly what their plans are for folks in your situation who need more specific assistance. Not everyone learns the same way. I hope they have more than one education plan in mind. Do you ever study as a group?