Question

Factor the expression over the complex numbers." title=" x^{2} +18" alt=" x^{2} +18" align="absmiddle" class="latex-formula">

Answer 1

Here we are given the expression:

$x^{2}+18$

Now let us equate it to zero to find x first,

$x^{2}+18=0$

Now subtracting 18 from the other side,

$x^{2}=-18$

taking square root on both sides,

So we will get two values of x as ,

$x=3\sqrt{-2}$

$x=-3\sqrt{-2}$

Now we can write square root -1 as i,

So our factors become,

$x=3i\sqrt{2}$

$x=-3i\sqrt{2}$

Answer:

The final factored form becomes,

$(x+3i\sqrt{2})(x-3i\sqrt{2})$

Answer 2

Answer:

$(x+3i\sqrt{2})(x-3i\sqrt{2})$

Step-by-step explanation:

1. You must apply the Quadratic formula, which is:

$x=\frac{-b+/-\sqrt{b^{2}-4ac} }{2a}$

2. Substitute values:

$a=1\\b=0\\c=18$

$x=\frac{-0+/-\sqrt{0^{2}-4(1)(18)} }{2(1)}\\x=\frac{+/-\sqrt{-72}}{2}\\x=\frac{+/-6i\sqrt{2}}{2}\\x=+/-3i\sqrt{2}$

3. Finally, you obtain:

$(x+3i\sqrt{2})(x-3i\sqrt{2})$