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Thread: (Algebra I) Confused about factoring polynomials

  1. #1
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    (Algebra I) Confused about factoring polynomials

    Hello all,

    So far I have a fairly good understanding of factoring two and three term polynomials (I thought I did). I can find the GCF and understand how it applies. I've been solving the following types of problems through my homework:
    -9a5 + 18a2 - 3a = -3a(3a4 - 6a + 1) and 5x4 - 20x = 5x (x3 - 4).

    But textbook suddenly showed:
    Factor: 5(x + 3) + y(x + 3)

    Solution:
    The binomial (x + 3) is the greatest common factor. Use the distributive property to factor out (x + 3).

    5(x + 3) + y(x + 3) = (x + 3) (5 + y)

    My problem:
    I don't understand how (x + 3) is a factor because so far, I've only see factors to be whole numbers and variables. How do you find a GCF from (x + 3)?? Is this an example of factoring by grouping? That's in the next section so I haven't covered that yet.

    I really want to understand this section before I get back into class so that my professor's examples make more sense.

    Thank you.
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  2. #2
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    Re: (Algebra I) Confused about factoring polynomials

    Suppose u=x+3. Then, you have 5u+yu = u(5+y). Replace u by (x+3). If you want to see it with whole numbers, plug in x=0. Try again for x=1. Keep trying for various values of x until you spot a pattern. A large part of learning Mathematics is training your brain to spot patterns quickly.

    My point with the replacement of x+3 with u was that you can start to think of (x+3) as a variable, as well. In this case, u is a dependent variable (it depends on the value of x) while x is an independent variable (we have no variables listed upon which the value of x depends).
    Last edited by SlipEternal; Oct 30th 2017 at 12:45 PM.
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  3. #3
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    Re: (Algebra I) Confused about factoring polynomials

    Doesn't you book have a definition of the word "factor"? If it does, you should realize that there is no requirement that a factor be a single term.
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  4. #4
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    Re: (Algebra I) Confused about factoring polynomials

    Quote Originally Posted by HallsofIvy View Post
    Doesn't you book have a definition of the word "factor"? If it does, you should realize that there is no requirement that a factor be a single term.
    No it doesn't but I understand what you mean. Thanks


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