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factor(x^{2}-1+3x)
Subtract 2 from 1 to get -1.
x^{2}+3x-1=0
Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.
x=\frac{-3±\sqrt{3^{2}-4\left(-1\right)}}{2}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x=\frac{-3±\sqrt{9-4\left(-1\right)}}{2}
Square 3.
x=\frac{-3±\sqrt{9+4}}{2}
Multiply -4 times -1.
x=\frac{-3±\sqrt{13}}{2}
Add 9 to 4.
x=\frac{\sqrt{13}-3}{2}
Now solve the equation x=\frac{-3±\sqrt{13}}{2} when ± is plus. Add -3 to \sqrt{13}.
x=\frac{-\sqrt{13}-3}{2}
Now solve the equation x=\frac{-3±\sqrt{13}}{2} when ± is minus. Subtract \sqrt{13} from -3.
x^{2}+3x-1=\left(x-\frac{\sqrt{13}-3}{2}\right)\left(x-\frac{-\sqrt{13}-3}{2}\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-3+\sqrt{13}}{2} for x_{1} and \frac{-3-\sqrt{13}}{2} for x_{2}.
x^{2}-1+3x
Subtract 2 from 1 to get -1.