Question

Factor the expression over the complex numbers. x^2+52

Answer 1

Here we are given the expression:

$x^{2}+52$

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

$x^{2}+52=0$

Now subtracting 52 from the other side,

$x^{2}=-52$

taking square root on both sides,

So we will get two values of x as ,

$x=+2\sqrt{-13}$

$x=-2\sqrt{-13}$

Now we can write square root -1 as i,

So our factors become,

$x=+2i\sqrt{13}$

$x=-2i\sqrt{13}$

Answer:

The final factored form becomes,

$(x+2i\sqrt{13})(x-2i\sqrt{13})$