How to factorise this

[Joshcanread]

How do you factorise this 

 

(x-6)² - 11

[Dash Lambda]

7 hours ago, VegetableStu said:

1. expand (x-6)²
2. simplify the constants
3. complete the square use the quadratic equation

That works, but it's not the way I suggest. The expression he's starting with is already halfway to the quadratic formula. It's actually more work to expand it then plug&chug.

 

OP, think about it this way:

Factoring a polynomial means breaking it into its roots. So if your function equals 0 at x=r₁ and x=r₂ then you'll break it into (x - r₁)(x - r₂).

That means your goal is to solve (x - 6)² - 11 = 0.

To make that easier, first ignore the 6: How would you solve x² - 11 = 0?

Then put the 6 back in: If the solution to x² - 11 = 0 is x = c, how would you solve x - 6 = c?

 

Then you've got your roots.