Question

+ 2 \sqrt{2}x - 6 " alt=" {x}^{2} + 2 \sqrt{2}x - 6 " align="absmiddle" class="latex-formula">
factorise pls​

Answer 1

Answer:

The two factors are (x - √2) and (x + 3√2).

Step-by-step 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.