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
+ bx+ c = 0 .
are the roots of this equation, then
+ 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
= –1 and x2
= 3. Hence, 2x2 – 4x – 6 = 2 ( x
+ 1 ) ( x – 3 ) .
( Open the brackets and check the result, please ).