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

1 Answer
Jim G.
Apr 11, 2018

#(x+1+sqrt2i)(x+1-sqrt2i)#

Explanation:

#"there are no whole number factors for + 3 which sum to + 2"#

#"factor using the solutions to "x^2+2x+3=0#

#"solve using the "color(blue)"quadratic formula"#

#"with "a=1,b=2" and "c=3#

#x=(-2+-sqrt(4-12))/2#

#color(white)(x)=(-2+-sqrt(-8))/2=(-2+-2sqrt2i)/2=-1+-sqrt2i#

#rArr(x-(-1+sqrt2i))(x-(-1-sqrt2i))#

#rArrx^2+2x+3=(x+1+sqrt2i)(x+1-sqrt2i)#

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