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I really want to understand factoring, and I have a problem and the answer but I don't understand the steps to getting an answer. 3x^5-12^4+18x^3

  • Math -

    The first thing to do, to make life simpler, is to factor out any constant, so you are working with smaller numbers. That gives you


    Now note that all the powers of x are at least 3, meaning you can factor out an x^3:


    At this point you can struggle to find the factors, or note first that the discriminant is

    16-24 = -8

    which is negative, so you know that you cannot factor it any further, using real numbers.

  • Math -

    3x^5 - 12x^4 + 18x^3.

    1. Locate the smallest constant which is
    3. If 3 will divide into the other constants with no remainder, factor out 3.

    2. Factor out the variable with the smallest exponent which is x^3.
    We have factored out 3x^3.

    3. To determine what goes inside of the parenthesis, divide each term by 3x^3
    and get:

    3x^3(x^2 - 4x + 6).

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