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Thread: Few questions about factoring ?

  1. #1
    Junior Member brandnew's Avatar
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    Few questions about factoring ?

    When simplifying fractions ?Do we make use of prime factorization ?

    Does this below list cover all the methods of Factoring ?

    Factoring polynomials

    ’To factor’ means to break up into multiples.

    Factors of natural numbers

    You will remember what you learnt about factors in Class VI. Let us take a natural number,
    say 30, and write it as a product of other natural numbers, say
    30 = 2 × 15
    = 3 × 10 = 5 × 6
    Thus, 1, 2, 3, 5, 6, 10, 15 and 30 are the factors of 30.
    Of these, 2, 3 and 5 are the prime factors of 30 (Why?)
    A number written as a product of prime factors is said to
    be in the prime factor form; for example, 30 written as
    2 × 3 × 5 is in the prime factor form.
    The prime factor form of 70 is 2 × 5 × 7.
    The prime factor form of 90 is 2 × 3 × 3 × 5, and so on.
    Similarly, we can express algebraic expressions as products of their factors. This is
    what we shall learn to do in this chapter.


    Factors of algebraic expressions

    We have seen in Class VII that in algebraic expressions, terms are formed as products of
    factors. For example, in the algebraic expression 5xy + 3x the term 5xy has been formed
    by the factors 5, x and y, i.e.,
    5xy = 5 * x * y
    Observe that the factors 5, x and y of 5xy cannot further
    be expressed as a product of factors. We may say that 5,
    x and y are ‘prime’ factors of 5xy. In algebraic expressions,
    we use the word ‘irreducible’ in place of ‘prime’. We say that
    5 × x × y is the irreducible form of 5xy. Note 5 × (xy) is not
    an irreducible form of 5xy, since the factor xy can be further
    expressed as a product of x and y, i.e., xy = x × y.

    What is Factorisation?
    When we factorise an algebraic expression, we write it as a product of factors. These
    factors may be numbers, algebraic variables or algebraic expressions.
    Expressions like 3xy, 5x2y , 2x (y + 2), 5 (y + 1) (x + 2) are already in factor form.
    Their factors can be just read off from them, as we already know.
    On the other hand consider expressions like 2x + 4, 3x + 3y, x2 + 5x, x2 + 5x + 6.
    It is not obvious what their factors are. We need to develop systematic methods to factorise
    these expressions, i.e., to find their factors.



    Methods of Factoring

    Method of common factors
    Factorisation by regrouping terms
    Factorisation using identities
    Factors of the form ( x + a) ( x + b)
    Factor by Splitting






















    Factorise 6x2 + 17x + 5 by splitting the middle term

    (By splitting method) : If we can find two numbers p and q such that
    p + q = 17 and pq = 6 × 5 = 30, then we can get the factors

    So, let us look for the pairs of factors of 30. Some are 1 and 30, 2 and 15, 3 and 10, 5
    and 6. Of these pairs, 2 and 15 will give us p + q = 17.

    So, 6x2 + 17x + 5 = 6x2 + (2 + 15)x + 5
    = 6x2 + 2x + 15x + 5
    = 2x(3x + 1) + 5(3x + 1)
    = (3x + 1) (2x + 5)




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  2. #2
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    Re: Few questions about factoring ?

    I am not going to read all of that. If you have a specific question, we can answer it. I doubt anyone is going to read an entire entry from a textbook or a help website and try to figure out what your question is from that.
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  3. #3
    Junior Member brandnew's Avatar
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    Re: Few questions about factoring ?

    When simplifying fractions ?Do we make use of prime factorization ?

    Does the above list cover all the methods of Factoring ?
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    Re: Few questions about factoring ?

    Quote Originally Posted by brandnew View Post
    When simplifying fractions ?Do we make use of prime factorization ?
    If you choose to use prime factorization, then you may. This question does not make sense, and I suspect it is not what you are really trying to ask, but I cannot fathom what that may be.

    Quote Originally Posted by brandnew View Post
    Does the above list cover all the methods of Factoring ?
    Again, this question does not make sense. It does not cover any methods of factoring which have not yet been discovered. It likely covers a list of methods that have been discovered. Because I do not know of any comprehensive list of all methodologies for anything, I doubt this question has an answer. Again, it is likely that I just do not understand what you are really trying to ask.
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    Junior Member brandnew's Avatar
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    Re: Few questions about factoring ?

    Sorry a bunch of noob questions , so that i can try to learn algebra properly .I had to start somewhere , i thought i would start by simplifying fractions , then move to simplifying expressions , and to solving algebraic equations
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    Re: Few questions about factoring ?

    Learning on your own, or classroom?
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  7. #7
    Junior Member brandnew's Avatar
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    Re: Few questions about factoring ?

    Learning on my own , books from this website

    http://ncert.nic.in/textbook/textbook.htm
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  8. #8
    Junior Member brandnew's Avatar
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    Re: Few questions about factoring ?

    I think i finally figured out where to start , That 6th grade book in that website has a lot of information about fractions .

    I guess i should start like this

    GCF
    Fractions
    Algebraic expressions
    Algebraic equations
    Last edited by brandnew; May 17th 2017 at 11:29 AM.
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