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EQUATIONS -> Factoring of a quadratic trinomial


  • Equations: common information

  • Main ways used at solving of equations

  • Linear equations

  • Quadratic equation

  • Solution of a quadratic equation

  • Properties of roots of a quadratic equation. Viete's theorem

  • Factoring of a quadratic trinomial

    Factoring of a quadratic trinomial


    Each quadratic trinomial  ax2 + bx+ c  can be resolved to factors of the first degree by the next way. Solve the quadratic equation

    ax2 + bx+ c = 0 .

    If    x1  and  x2   are the roots of this equation, then

    ax2 + bx+ c = a ( x –  x1 ) ( x –  x2 ) .

    This affirmation can be proved using either formulas for roots of a non-reduced quadratic equation or Viete’s theorem.  ( Check it, please ! ) .

    E x a m p l e .  Resolve to the first degree factors the trinomial: 2x2 – 4 x – 6.

    S o l u t i o n . At first we solve the equation:  2x2 – 4x – 6 = 0 .  Its roots are:
                           x    1 = –1 and  x2 = 3.  Hence, 2x2 – 4x – 6 = 2 ( x + 1 ) ( x – 3 ) .
                          ( Open the brackets and check the result, please ).

  • Equations of higher degrees