Factoring of a quadratic trinomial
Each quadratic trinomial ax 2 + bx+ c can be resolved to factors of the first degree by the next way. Solve the quadratic equation
If x 1 and x 2 are the roots of this equation, then
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: 2 x 2 – 4 x – 6.
S o l u t i o n . At first we solve the equation: 2
x
2
– 4
x
– 6 = 0 . Its
roots are:
x
1
=
–
1 and
x
2
= 3. Hence, 2
x
2
– 4
x
– 6 = 2 (
x
+ 1 ) (
x
– 3 ) .
( Open the brackets and check the result, please ).