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General Advice for Factoring Polynomials By Patrica Hensley - Jefferson Davis Campus

  1. Always factor out the greatest common factor first.
  2. If the polynomial to be factored is a binomial, then it may be a difference of two squares or a sum or difference of two cubes (remember that a sum of two squares does not factor).


  3. Two terms

    Difference of Squares

    Sum of Cubes

    Difference of Cubes

    x2 y2 = (x y) (x + y)

    x3 + y3 = (x + y)(x2 xy +y2)

    x3 y3 = (x y) (x2 + xy +y2)

    Ex. 4x2 9 = (2x 3)(2x + 3)

    Ex. 8y3 + 27 =

    (2y + 3)(4y2 6y + 9)

    Ex. 216x3 125 =

    (6x 5)(36x2 + 30x +25)



  4. If the polynomial to be factored is a trinomial, then
    1. If two of the three terms are perfect squares, the polynomial may be a perfect square.
    2. Otherwise, the polynomial may be one of the general forms.


    Three Terms

    Perfect Square Trinomial

    Trinomial

    x2 + 2xy + y2 = (x + y)2

    Ex. 36x2 + 60x +25 = (6x + 5)2

    ax2 + bx + c

    Ex. 6k2 + 5kp 6p2 = (3k 2p)(2k + 3p)

    x2 2xy + y2 = (x y)2

    Ex. x2 6x + 9 = (x 3)2

     


  5. If the polynomial to be factored consists of four or more terms, then try factoring by grouping.
  6. Four Terms

    May factor by grouping

    Ex. 10ab 6b + 35a 21 = 2b(5a 3) + 7(5a 3) = (5a 3) (2b + 7)

     

    5. Can any factors be factored further?