Question

How do you factor `2x^2+5x-30`?

Answer 1

`2x^2+5x-30 = 1/8(4x+5-sqrt(265))(4x+5+sqrt(265))`

Explanation:

Complete the square, first premultiplying by `8` to cut down on fraction arithmetic, not forgetting to divide by `8` at the end:

`8(2x^2+5x-30)`

`=16x^2+40x-240`

`=(4x)^2+2(4x)(5)-240`

`=(4x+5)^2-25-240`

`=(4x+5)^2-265`

`=(4x+5)^2-(sqrt(265)^2)`

`=((4x+5)-sqrt(265))((4x+5)+sqrt(265))`

`=(4x+5-sqrt(265))(4x+5+sqrt(265))`

Dividing both ends by `8`, we find:

`2x^2+5x-30 = 1/8(4x+5-sqrt(265))(4x+5+sqrt(265))`