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how to factorize x^4-3x^3-5x^2+3x+4?

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Jers15viz
Use synthetic division:
(x^4-3x^3-5x^2+3x+4)/(x-1)=x^3-2x^2-7x-4
(x^3-2x^2-7x-4)/(x+1)=x^2-3x+4
x^2-3x+4=0
x^2-3x=-4
x^2-3x+9/4=-4+9/4
(x-3/2)^2=-7/4
x-3/2=√7/4, -√7/4
x=√7/4 +3/2, -√7/4+3/2

The factors are:
(x-1)(x+1)(x-[√7+6/4])(x+[√7+6/4])