Factoring Quadratic Polynomials into Linear Factors

If `x_1` and `x_2` are the roots of quadratic polynomial of `ax^2+bx=c` (i.e.the root of equation of `ax^2+bx+c=0`), then `color(blue)(ax^2+bx+c=a(x-x_1)(x-x_2))`.This is the formula of factoring quadratic polynomial into factors.

Example. Factor the following: `6x^2-x-2`.

We apply the formula of roots of quadratic equation to the equation of `6x^2-x-2=0` and find `x_1=-1/2, x_2=2/3`. So,

`6x^2-x-2=6(x+1/2)(x-2/3)=2(x+1/2)*3(x-2/3)=(2x+1)(3x-2)`.