Math

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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

    3(x^5-4x^4+6x^3)

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

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

    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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