Question

How do you factor `x^2 + 8x - 19`?

Answer 1

`x^2+8x-19=(x+4-sqrt(35))(x+4+sqrt(35))`

Explanation:

Complete the square and use the difference of squares identity:

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

with `a=(x+4)` and `b=sqrt(35)` as follows:

`x^2+8x-19`

`=(x+4)^2-4^2-19`

`=(x+4)^2-16-19`

`=(x+4)^2-35`

`=(x+4)^2-(sqrt(35))^2`

`=((x+4)-sqrt(35))((x+4)+sqrt(35))`

`=(x+4-sqrt(35))(x+4+sqrt(35))`