Question

How do you factor `6x^2-21`?

Answer 1

`6x^2-21 = 3(sqrt(2)x-sqrt(7))(sqrt(2)x+sqrt(7))`

Explanation:

The difference of squares identity can be written:

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

We use this with `a=sqrt(2)x` and `b=sqrt(7)` as follows:

`6x^2-21 = 3(2x^2-7)`

`color(white)(6x^2-21) = 3((sqrt(2)x)^2-(sqrt(7))^2)`

`color(white)(6x^2-21) = 3(sqrt(2)x-sqrt(7))(sqrt(2)x+sqrt(7))`