unfortunately there's no, that is of corse if you don't know the roots of the polynomial beforehand.easier way than this
Actually I don't know why do you insist on factorizing the polynomial, when a simple formula already exists for findingg the roots of a quadratic equation.
you might also read about:
Vieta's Formulas -- from Wolfram MathWorld
Here's another method that works, but only does so if the roots of the equation are rational numbers or integers.
This is called the "ac" method.
Multiply the leading coefficient by the constant coefficient. In this case
Now write all the pairs of factors of -14:
Now look for a pair that sums to the coefficient of the linear term, in this case -5. Note that 2 + (-7) = -5. (If such a pair does not exist, then the equation cannot be factored in terms of rational numbers.)
So we want to write the linear term as
[tex]-5x = (2 - 7)x = 2x - 7x
in the original quadratic.
Now factor by grouping:
Now you can solve this by setting each factor independently equal to 0.