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FACTORISING, which type do i use, when to find value of x and when to not?? Watch

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    As you can probably tell by the title im VERY confused, the more i revise it the more confused i get. There are 2 different types fo factorising i can use when the value of x>1, quadratic formula or the one where i multiply a by c and get two value that multiply to make c and add to give b. But what do i do when my c value is smaller than my b?? eg. 14x^2-45x-42=0 (42 came from me multiplying a (14) by my original c (3) if I can't solve this (on a non calc) using the factorising method just discussed do I just leave it as =) or is there another method to use??? IKNOW this must be so confusing to read but please HELP! I HATE MATHS
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    (Original post by victoriakc)
    As you can probably tell by the title im VERY confused, the more i revise it the more confused i get. There are 2 different types fo factorising i can use when the value of x>1, quadratic formula or the one where i multiply a by c and get two value that multiply to make c and add to give b. But what do i do when my c value is smaller than my b?? eg. 14x^2-45x-42=0 (42 came from me multiplying a (14) by my original c (3) if I can't solve this (on a non calc) using the factorising method just discussed do I just leave it as =) or is there another method to use??? IKNOW this must be so confusing to read but please HELP! I HATE MATHS
    why did u times 14 by c and put it where c was? That's not how it works. Give me an example you are struggling with and i can go through it for you.
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    (Original post by victoriakc)
    As you can probably tell by the title im VERY confused, the more i revise it the more confused i get. There are 2 different types fo factorising i can use when the value of x>1, quadratic formula or the one where i multiply a by c and get two value that multiply to make c and add to give b. But what do i do when my c value is smaller than my b?? eg. 14x^2-45x-42=0 (42 came from me multiplying a (14) by my original c (3) if I can't solve this (on a non calc) using the factorising method just discussed do I just leave it as =) or is there another method to use??? IKNOW this must be so confusing to read but please HELP! I HATE MATHS
    OK then...

    Yes, when you have a quadratic ax^2+bx+c, you can use the quadratic formula to find the roots x_1,x_2 to then just factorise your quadratic into (x-x_1)(x-x_2)

    The other way, as you say, is to use inspection on the values of b and ac. Since you are confused about the case when c<b, take the quadratic 8x^2+2x-1=(2x+1)(4x-1) but let's pretend we don't know the RHS for the time being. So to determine what the factorised form of our quadratic is, let's first factor out \frac{1}{8} out of our quadratic to get \frac{1}{8}(8^2x^2+2\cdot 8x -8)=\frac{1}{8}((8x)^2+2(8x)-8). Let's call y=8x, then our quadratic is simply \frac{1}{8}(y^2+2y-8). Note now that here b is unchanged but our constant value is the same as ac from our original.

    Now we want to look for two values, \lambda, \mu which give: \lambda + \mu = b =2 and \lambda \mu = ac = -8. You should know that \lambda = 4 and \mu = -2 do the job. So then all is left is you put those values in there by saying that \frac{1}{8}(y+4)(y-2). Here we pretty much have what we want, all is left is to sub back y=8x and we get \frac{1}{8}(8x+4)(8x-2). Now factoring out 4 out of the first bracket, and 2 out of the second bracket, we get \frac{1}{8}\cdot 4 \cdot 2 \cdot (2x+1)(4x-1)=(2x+1)(4x-1). Job done.

    This is much quicker in practice but I've described to you the whole recipe in detail.

    To do it quickly, you'd just do: 8x^2+2x-1=\frac{1}{8}((8x)^2+2(8x)-8)=\frac{1}{8}(8x+4)(8x-2)=(2x+1)(4x-2)

    Get it?

    Also in your title with the "when to find the value of x" doesn't make much sense unless you are solving an equation with a variable x in your quadratic.
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    (Original post by RDKGames)
    OK then...

    Yes, when you have a quadratic ax^2+bx+c, you can use the quadratic formula to find the roots x_1,x_2 to then just factorise your quadratic into (x-x_1)(x-x_2)

    The other way, as you say, is to use inspection on the values of b and ac. Since you are confused about the case when c<b, take the

    Also in your title with the "when to find the value of x" doesn't make much sense unless you are solving an equation with a variable x in your quadratic.
    How on earth is this helping? Why over complicate this so much? Please think about 'audience' when you post ....
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    (Original post by victoriakc)
    As you can probably tell by the title im VERY confused, the more i revise it the more confused i get. There are 2 different types fo factorising i can use when the value of x>1, quadratic formula or the one where i multiply a by c and get two value that multiply to make c and add to give b. But what do i do when my c value is smaller than my b?? eg. 14x^2-45x-42=0 (42 came from me multiplying a (14) by my original c (3) if I can't solve this (on a non calc) using the factorising method just discussed do I just leave it as =) or is there another method to use??? IKNOW this must be so confusing to read but please HELP! I HATE MATHS
    When we just factorise we just have an expression ie no equation.

    Solving is for the situation where we have an equation and often factorising is the first step. However, if you are struggling to solve and can't find the factorisation quickly or it doesn't factorise then use the formula.

    Which year are you in? I'll post more detail once I know which exam you are aiming at.
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    (Original post by Muttley79)
    How on earth is this helping? Why over complicate this so much? Please think about 'audience' when you post ....
    Overcomplicate what? I literally just explained the process in all the detail that there is for them to know, nothing there should be out of reach of a GCSE student. If they misunderstand something they can ask.

    I'd think it's helping because OP doesn't know how to factorise quadratics with a>0, and apparently when c<b for some reason, so I just gave them an example. I was hesitant to go into the finer details because I recognised the audience.

    If it misses their question, then it was phrased very badly and I misunderstood (quite frankly their post is a mess)
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    (Original post by RDKGames)
    Overcomplicate what? I literally just explained the process in all the detail that there is for them to know, nothing there should be out of reach of a GCSE student. If they misunderstand something they can ask.

    I'd think it's helping because OP doesn't know how to factorise quadratics with a>0, and apparently when c<b for some reason, so I just gave them an example. I was hesitant to go into the finer details because I recognised the audience.

    If it misses their question, then it was phrased very badly and I misunderstood (quite frankly their post is a mess)
    Why introduce greek letters?

    If you aren't clear what they are asking then don't post a reply!
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    (Original post by Muttley79)
    Why introduce greek letters?

    If you aren't clear what they are asking them don't post a reply!
    That's just my norm, if OP don't know what they are, then again, OP can ask.

    As far as I'm concerned, at least one of their questions in their post was about "what to do when..." factorising a certain quadratic on which I gave an example on, and they made that pretty clear, but I'm not sure if there was anything else/different they wanted due to their messy post.

    Please don't assume the post will not be helpful to them, they can always ask for more info or ignore it completely.
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    (Original post by RDKGames)
    Overcomplicate what? I literally just explained the process in all the detail that there is for them to know, nothing there should be out of reach of a GCSE student. If they misunderstand something they can ask.

    I'd think it's helping because OP doesn't know how to factorise quadratics with a>0, and apparently when c<b for some reason, so I just gave them an example. I was hesitant to go into the finer details because I recognised the audience.

    If it misses their question, then it was phrased very badly and I misunderstood (quite frankly their post is a mess)
    The method they are using in school is almost certainly not the method you gave. It seems like they are using the AC method.

    But to be fair, I think the OP needs to give an example so that we can help. Trying to explain the whole topic of factorising quadratics on an internet forum to a GCSE student isn't the best idea.
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    (Original post by Notnek)
    The method they are using in school is almost certainly not the method you gave. It seems like they are using the AC method.

    But to be fair, I think the OP needs to give an example so that we can help. Trying to explain the whole topic of factorising quadratics on an internet forum to a GCSE student isn't the best idea.
    I agree with the example part, the one they gave has no roots and not sure how it was gotten. Though there's a few methods of concerning the use of ac so I'm uncertain of which they used or were taught to use. Wish they made their post clearer, I just went with one of them, maybe it's a new method to have under their belt then.
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    (Original post by RDKGames)
    I agree with the example part, the one they gave has no roots and not sure how it was gotten. Though there's a few methods of concerning the use of ac so I'm uncertain of which they used. Wish they made their post clearer, I just went with one of them, maybe it's a new method to have under their belt then.
    The "AC method" will almost always be the method where you split the bx term up and then factorise by grouping. While the use of a "disguised quadratic" is quite a nice method, I think it might be beyond the average GCSE student.
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    (Original post by victoriakc)
    As you can probably tell by the title im VERY confused, the more i revise it the more confused i get. There are 2 different types fo factorising i can use when the value of x>1, quadratic formula or the one where i multiply a by c and get two value that multiply to make c and add to give b. But what do i do when my c value is smaller than my b?? eg. 14x^2-45x-42=0 (42 came from me multiplying a (14) by my original c (3) if I can't solve this (on a non calc) using the factorising method just discussed do I just leave it as =) or is there another method to use??? IKNOW this must be so confusing to read but please HELP! I HATE MATHS
    It doesn't matter if c is smaller than b. That doesn't affect anything. For example, x^2 + 2x + 3 = 0 has c larger than b, but it's straightforward to factorise (x+1)(x+2).

    As a general rule, calculate b^2 - 4ac first. Here's what to do:
    1. If it's negative... check your calculations. Then check that you aren't sitting a Further Maths paper. Then cry.
    2. If it's zero... you should be able to do it by factorising, but you can use whatever method you want.
    3. If it's a square number... you should also be able to do it by factorisng.
    4. If it isn't square... you can't factorise it easily - you have to either complete the square or use the formula.

    I prefer using the formula over completing the square, and I advise you to do this when you have a choice. Of course if you're told to do a certain method, you have to do it that way.
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    Im in year 11 sitting the wjec Higher paper (New Wales)
    (Original post by Muttley79)
    When we just factorise we just have an expression ie no equation.

    Solving is for the situation where we have an equation and often factorising is the first step. However, if you are struggling to solve and can't find the factorisation quickly or it doesn't factorise then use the formula.

    Which year are you in? I'll post more detail once I know which exam you are aiming at.
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    (Original post by victoriakc)
    Im in year 11 sitting the wjec Higher paper (New Wales)
    OK

    Can you give some examples? I think we'll be able to help you better and understand where you are stuck.
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    You can use any factorising technique as long as it gets you the x values. The reason that there are so many different techniques is because sometimes it is more appropriate and easier to use a certain technique over another. For example for fractions or decimals (e.g. x^2 + 19.4x - 376.75 = 0) completing the square or the quadratic formula may be easier than using the regular factorising technique. Also, when you cannot factorise through the regular technique, you can use the quadratic formula or completing the square. Often in GCSE questions they prompt you towards which method they want you to use, however if they do not then you have to use the easiest method for that question.

    You only solve for x when they state 'solve for x' or 'find the x values' or when the quadratic equation is = 0, you simply factorise and leave in brackets when it is not.

    The original quadratic equation was 14x^2-45x-3 I am guessing.
    You multiplied the c, -3, by 14 to make -42.
    So the factors of -42 that multiply to make -42 and add to make -45 cannot be found through the regular factorising technique. This means you have to do completing the square or use the quadratic formula.

    Have you been taught about the completing the square method or the quadratic formula?
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    wow OK. That was a bit rude! Im perfectly capapble of factorising and was doing fine until i came across this question, which in that case i searched up online how to do it since my normal method does not seem to work and in that paprt i had simply found too many posts explaining it in so many different ways that it just confused me so much more. All im really looking for is factors of 42 that also add to make 45 and also when i know i need to factorise fully to find x in a question or just factorise it to ax+bx+c=0. (if that soothes the MESS which is student panic enough for you!)
    (Original post by RDKGames)
    Overcomplicate what? I literally just explained the process in all the detail that there is for them to know, nothing there should be out of reach of a GCSE student. If they misunderstand something they can ask.

    I'd think it's helping because OP doesn't know how to factorise quadratics with a>0, and apparently when c<b for some reason, so I just gave them an example. I was hesitant to go into the finer details because I recognised the audience.

    If it misses their question, then it was phrased very badly and I misunderstood (quite frankly their post is a mess)
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    The question given is ' 8/2x-1 + 5x+9/3x+1 = 4 '
    using this i multiplied both denominators by each part which allowed me to cancel the bottom two denominators (so basically just cross multiplying however multiplying the 4 by both denominators as well)
    then i had 8(3x+1) + 5x+9(2x-1) = 4(3x+1) (2x-1)
    and i solved it from there doing FOIL
    then eventually i brought one half over to =0 then further solved that
    i was then left with 0=14x^2 - 45x -3
    at this stage i attempted to use the method that multiplies ac (14x-3=-42) and then these two factors must add to make b (45)
    and thats where i got into a bit of a mess- im pretty sure this question is a non-calc so i dont think i will be able to use the quadratic formula to solve it
    (Original post by Muttley79)
    OK

    Can you give some examples? I think we'll be able to help you better and understand where you are stuck.
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    This was very helpful thank you so much! I shall try both the quadratic and completing the square methods (however im not sure if this is a calculator paper so i may not be able to use the quadratic formula but i'll try it any way)
    (Original post by Deliciate)
    You can use any factorising technique as long as it gets you the x values. The reason that there are so many different techniques is because sometimes it is more appropriate and easier to use a certain technique over another. For example for fractions or decimals (e.g. x^2 + 19.4x - 376.75 = 0) completing the square or the quadratic formula may be easier than using the regular factorising technique. Also, when you cannot factorise through the regular technique, you can use the quadratic formula or completing the square. Often in GCSE questions they prompt you towards which method they want you to use, however if they do not then you have to use the easiest method for that question.

    You only solve for x when they state 'solve for x' or 'find the x values' or when the quadratic equation is = 0, you simply factorise and leave in brackets when it is not.

    The original quadratic equation was 14x^2-45x-3 I am guessing.
    You multiplied the c, -3, by 14 to make -42.
    So the factors of -42 that multiply to make -42 and add to make -45 cannot be found through the regular factorising technique. This means you have to do completing the square or use the quadratic formula.

    Have you been taught about the completing the square method or the quadratic formula?
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    (Original post by victoriakc)
    The question given is ' 8/2x-1 + 5x+9/3x+1 = 4 '
    using this i multiplied both denominators by each part which allowed me to cancel the bottom two denominators (so basically just cross multiplying however multiplying the 4 by both denominators as well)
    then i had 8(3x+1) + 5x+9(2x-1) = 4(3x+1) (2x-1)
    and i solved it from there doing FOIL
    then eventually i brought one half over to =0 then further solved that
    i was then left with 0=14x^2 - 45x -3
    at this stage i attempted to use the method that multiplies ac (14x-3=-42) and then these two factors must add to make b (45)
    and thats where i got into a bit of a mess- im pretty sure this question is a non-calc so i dont think i will be able to use the quadratic formula to solve it
    You should get 0 = 14x^2 - 41x - 3.

    Have another go and please post all your working if you get stuck. Also, for future questions please always post the original question and your full attempt.
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    You should be able use the quadratic formula even without a calculator by leaving your answer in surd form. However, completing the square is much easier than using the quadratic formula when you don't have a calculator in my opinion. As Notnek said, the quadratic should in fact have been 14x^2 - 41x - 3 = 0 so the regular factorising technique should work with that. However, if you are less confident with using the quadratic formula or completing the square then I advice doing practice questions on the quadratic formula and completing the square (particularly non-calculator) as you will eventually come across a question that requires you to use them.
 
 
 
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