Answer:
The two factors are (x - √2) and (x + 3√2).
Explanation:
I'd use the quadratic formula to find the roots of this expression first, and then make factors out of the resultant roots.
Here a = 1, b = 2√2 and c = -6.
Thus, the roots are:
-2√2 ± √[ (2√2)² - 4(1)(-6) ]
x = -------------------------------------------
2
which simplifies to:
-2√2 ± √32 -2√2 ± 4√2
x = ------------------- = -------------------- Reduce this to x = -√2 ± 2√2
2 2
The two roots are thus x = -√2 + 2√2 and x = -√2 - 2√2, or, after more simplification,
x = √2 and x = -3√2
If x = √2, then the corresponding factor of the given expression is:
(x - √2).
If x = -3√2, then the corresponding factor is (x + 3√2).
The two factors are (x - √2) and (x + 3√2).
When multiplied together, they yield x² + 2√2x - 6.