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    I want to learn as-level maths, self-taught, at home. So, I decided to buy " Cambridge A level mathematics for aqa student book 1 (AS/year 1)".

    this is for the new linear spec I've been hearing about.

    I've come from gcse, obviously, which I'm fairly competent in.

    they offer two quick examples of an equation on the first page, which I can do. then in the exercise part to part 1, with said examples, they throw this at me:

    X3 - 4x2 - 3x + 18 = (x+a)(x+b)2 for all x. Find the value of a and b.

    Am I supposed to know how to do this? Because it offers no prior knowledge to something like this on the first page.

    What am I missing here?

    the worked example, which is supposed to of "taught me" how to do this is as follows:
    2x^2 + 12x - 3 = a(x + p)^2 + q . find the values of a,p and q.

    bit different, right? or is it just me.

    I have no idea how to do this. I've been on it a week trying to understand it. is there a better of learning this, because, far as I can tell, this book assumes a great deal of knowledge about the reader.
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    That's higher level gcse maths, you should probably start there first.
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    (Original post by Azzyh)
    I want to learn as-level maths, self-taught, at home. So, I decided to buy " Cambridge A level mathematics for aqa student book 1 (AS/year 1)".

    this is for the new linear spec I've been hearing about.

    I've come from gcse, obviously, which I'm fairly competent in.

    they offer two quick examples of an equation on the first page, which I can do. then in the exercise part to part 1, with said examples, they throw this at me:

    X3 - 4x2 - 3x + 18 = (x+a)(x+b)2 for all x. Find the value of a and b.

    Am I supposed to know how to do this? Because it offers no prior knowledge to something like this on the first page.

    What am I missing here?

    the worked example, which is supposed to of "taught me" how to do this is as follows:
    2x^2 + 12x - 3 = a(x + p)^2 + q . find the values of a,p and q.

    bit different, right? or is it just me.

    I have no idea how to do this. I've been on it a week trying to understand it. is there a better of learning this, because, far as I can tell, this book assumes a great deal of knowledge about the reader.
    Two tricks you can use are:
    1: Multiply out:

     (x+a)(x+b)^{2},

    then compare the coeffifients on the powers of x.

    2: Substitute in small values for x and if the sum is 0 (say x=a), then you found a factor (x-a).
    then you can use long division to find a quadratic which you may then be able to factorise further.

    Spoiler:
    Show


    Constant term of the polynomial is 18. By comparing coefficients:  ab^{2} = 18.

 
 
 
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