How do you factor #x^2 + 2x +3#?

2 Answers
Jul 30, 2015

#(x+1+isqrt(2))(x+1-isqrt(2))#

Explanation:

Solve for the roots. First complete the square:

#x^2+2x+3=(x+1)^2+2=0#

Solve for #x#:

#(x+1)^2+2=0#

=>

#(x+1)^2=-2#

=>

#x+1=+-isqrt(2)#

=>

#x=-1+-isqrt(2)#

Therefore the factorisation is:

#(x+1+isqrt(2))(x+1-isqrt(2))#

Jul 30, 2015

Factor #y = x^2 + 2x + 3#

Explanation:

#D = b^2 - 4ac = 4 - 12 = - 8 < 0.#
Therefor, this function can't be factored.