Question

How do you factor `15x^2 - x-2`?

Answer 1

`15x^2-x-2=(3x+1)(5x-2)`

Explanation:

To factorize a quadratic polynomial `ax^2+bx+c`, if the discriminant `b^2-4ac` is a square f a rational number, then one can factorize it by splitting `b` in two parts whose product is `ac`.

Here discriminant is `(-1)^2-4*15*(-2)=1+120=121=11^2`, hence, one should split `15*(-2)=-30` in two parts so that their sum is `-1`. It is obvious these are `-6` and `5`.

Hence, `15x^2-x-2`

= `15x^2-6x+5x-2`

= `3x(5x-2)+1(5x-2)`

= `(3x+1)(5x-2)`