Question

what does x^2+1 factor to

Answer 1

Answer:

(x-i)(x+i)

Step-by-step explanation:

first, put the equation equal to 0:

${x}^{2} + 1 = 0$

then get the x term alone on one side:

${x}^{2} = - 1$

next, do the inverse operation to clean up the x term side, since x is to the 2nd power, we find the second (square) root of both sides:

$\sqrt{x^{2} } = \sqrt{ - 1}$

Simplify:

$x = i \: or \: x = - i$

Add/subtract the imaginary numbers to bring them with the x term again.

$(x - i)(x + i) = 0$

For this problem, you can just drop the "=0" part now that it's factored:

$(x - i)(x + i)$