factor x^4+3x^2+2

You might find it easier if you replace the x² with y

then you have y²+3y+2

You need two numbers that multiply to 2 and add to 3. they'll be 2 and 1

(y+2)(y+1)    but y=x²

(x²+2)(x²+1)

x⁴ + 3x² +2 = (x² + 1)(x² + 2)