Question

How do you factor `15x^2-9x-14`?

Answer 1

`15x^2-9x-14 = 1/60(30x-9-sqrt(921))(30x-9+sqrt(921))`

Explanation:

Here's how you can do it by completing the square. I will use `60 = 15*2^2` as a multiplier to allow me to work mostly in integers. Then use the difference of squares identity:

`a^2-b^2 = (a-b)(a+b)`

with `a=(30x-9)` and `b=sqrt(921)` as follows:

`15x^2-9x-14 = 1/60(900x^2-540x-840)`

`color(white)(15x^2-9x-14) = 1/60((30x)^2-2(30x)(9)+9^2-921)`

`color(white)(15x^2-9x-14) = 1/60((30x-9)^2-(sqrt(921))^2)`

`color(white)(15x^2-9x-14) = 1/60((30x-9)-sqrt(921))((30x-9)+sqrt(921))`

`color(white)(15x^2-9x-14) = 1/60(30x-9-sqrt(921))(30x-9+sqrt(921))`