# 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

*ax*

^{ 2 }

*+ bx+ c*= 0 .

If
*
x
*
_{
1
}
*
*
and
*
x
*
_{
2
}
*
*
are
*
*
the
*
*
roots of this equation, then

*ax*

^{ 2 }

*+ bx+ c = a*(

*x – x*

_{ 1 }) (

*x – x*

_{ 2 })

*.*

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 ).