My niece is being home-schooled for the 8th grade and has come across a 9th grade algebra question that she is clueless on. She called me to help, but even though I pulled an A in trig, algebras 1 and 2, and geometry, it has been 18 years since I have had any of it. I have looked at several sites hoping for an explanation that would jog my memory, but searching out factoring polynomials brings me to the conclusion that I need a remedial course! It seems like it might would make sense if I was in class and had just had this stuff, but seeing it cold without any prior chapter buildup makes no sense to me, and I surely couldn't explain it to an 8th grader to where she can understand enough to finish her other 15 problems. I think if I could have it explained to me in basic terms then I could get the same thing across to her. I have no intentions of doing the work for her, just trying to help so she can understand it and perform well on her quiz on it. Thank you in advance for any help that you can give me.

The problem is: 10x - 3 - 3x squared (don't know how to type squared- just looked like 3x2 LOL)

First, rearrange the terms in descending order ; 3x^2 + 10x - 3. Then apply what's known as the "reverse FOIL" method ; 3x^2 + 10x - 3 = (__ __)(__ __) ; two binomials whose product equals 3x^2 + 10x - 3. First, Outer, Inner, Last. First times First has to equal 3x^2. And there's only one way to get 3x^2. Last times Last has to equal -3. And there's only one way to get 3. Then Outer plus Inner has to equal 10x. So rearrange the last terms and the middle signs until you get a product of -3 and a sum of 10.

3x^2 + 10x - 3 can't be factored.

However, it's actually -3x^2 + 10x -3. Someone missed their morning coffee. :-)

Quote:

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Originally Posted by morgaine300

3x^2 + 10x - 3 can't be factored.

However, it's actually -3x^2 + 10x -3. Someone missed their morning coffee. :-)

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I stand corrected ; I missed the leading negative. I think I need stronger coffee:D. However, I'll now edit my initial response in light of this additional information. First of all, it is true that 3x^2 + 10x - 3 can't be factored ; I did not take that possibility into consideration as I did not actually attempt the problem, just provided an explanation how to do it. But, since it's actually -3x^2 + 10x -3, you'd begin by factoring out a -1 in order to eliminate that leading negative, which would make it -(3x^2 - 10x + 3). Then you'd proceed with the 3x^2 - 10x + 3 as described in my first response. Now, 3x^2 - 10x + 3 is factorable. I'm not going to give you the answer but let you figure it out for yourself. But when you think you have it, post it and I'll be glad to verify it or not for you.

(3x- -1) (x+3) doesn't look right but works out right, if I am doing my calcs correctly. Two negs make a positive if I recall correctly. If that is right, then your explanation was great! Thanks. I think I can explain it properly to my niece to help her out!

Nope, went back and checked work, and that did not work out right. Maybe I need some stronger coffee too!

I don't have any stronger coffee but I have some SunnyD sitting here if that helps.

You've got the concept going - you just need to go with it a bit further. If you factor out the -1, you must leave the -1 on your answer. That is -1(Ax +/- B)(Cx +/- D). Pulling out that -1 also changes all the signs of the 3 terms.

You've got the numbers - the signs are messed up. So that's where you need to be looking.

This is how I look at it. I look at the 3rd term first. If that's negative, I need a positive and a negative value to multiply to get a negative. When that is the case, I will need an outer and inner that subtract to get the middle term.

If the 3rd term is positive, then I need either two positives or two negatives. Since both signs will be the same, I will need an outer and inner that add to get the middle term. (I think in absolute values there cause it's easier.) Once I know the numbers I want, whether I need 2 positives or 2 negatives is determined by the middle term.

Re-writing yours properly:
(3x + 1)(x + 3)
Two positives make my last positive. Since the outer and inner are both positive, they have to add to get the 2nd term.
inner = 1 and outer = 9
Both positive so they add to get the middle term: 10
This isn't the correct answer, but just showing you what I mean, I hope.

So you've got a good start - you just have an issue with the signs and the dropped -1.

I don't know how much sense that makes. It's SO much easier to show that in person. (But then, most math is.)

My God! Seven posts and the OP is still not satisfied!

Ok rearrage, as previously told:



Factor -1, to give as previously said.

Then, factor , but don't forget the negative sign later on.

What are the possible factors of 3 (in 3x^2)? They are (1 x 3) and (-1 x -3)
What are the possible factors of 3 (in 3)? They are (1 x 3) and (-1 x -3)

Now, look at the middle term, -10x. That shows that you need to have some negative terms in the factors.

Usually, the factors of the term in x^2 is kept positive, so you have the factors:




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Now what you need to have is the result at the bottom. If you add the first upper factor by the first lower factor, you have -x and for the secod factors, you have -9x, which add up to -10x.

Then, take the diagonal factors and put them into brackets, like that:



When you expand, you'll have 3x^2-x-9x+3, which is the initial expression. Now, put it like this:



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Now, say I put it like that instead:




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Now, you have to multiply the diagonal factors to get -10x at the end. Therefore you'll take the vertical factors in brackets.

Summary of how to use that method: When you multiply the factors in vertical, take the diagonal in brackets. When you multiply the factors in diagonal, take the vertical factors in brackets. It always work.
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With practice, your daughter will get used to these, and will even be able to factorise such problems without any method. This will become something 'trivial', do not worry. I also had these problems some years ago, but now, I can do these with such an ease!

Hope you understand that method! :)

I was hitting such a brick wall on this. As previously posted, was getting the correct numbers, just the wrong signs. It had been way TOO long since I have had this stuff. After looking at it so long my eyes had started crossing, I finally used my last resort and called my high school Algebra teacher and he said this was an odd ? That had three possible answers.

factoring out the negative : -1(3x-1) (x-3) or keeping it in and using the negative in either parenthesis with the x as in either one of these possible answers: (-3x+1) (x-3) or (3x-1) (-x+3) any of the three work out the with the original answer.

I am not comfortable with these yet, but hopefully as I check my niece's answers, more of this will come back. I appreciate all the time and energy that you expending explaining this to me. I had never been to this site before but am adding it to my favorites as most people here are helpful! Thanks a bunch!

You're welcomed!

Concerning the problem, it's always easier to factor out the negative sign of the term with the highest power. That often makes the whole thing lots simpler!

If you have any more questions, feel free to ask! :)

All three of those do work and I came up with the (-3x + 1)(x - 3). However, it's more difficult to leave the negative on the first term cause it creates more possibilities to deal with. Much easier to factor out that -1 first.

And don't worry if it seems boggling. It kind of is like that, cause you're thinking about both what multiplies to get a set of numbers and at the same time can add up to get another number. It's a little odd to think about. :-) You almost have to do it all the time. I think you did well for how many years it's been!