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{x}^(2) + 2 √(2)x - 6
factorise pls​

User Zomnombom
by
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1 Answer

5 votes

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.

User Pramod Tapaniya
by
8.2k points

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