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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:
                       x1 = –1 and  x2 = 3.  Hence, 2x2 – 4x – 6 = 2 ( x + 1 ) ( x – 3 ) .
                      ( Open the brackets and check the result, please ).

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