Can you factor the following two polynomials?

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Can you factor the following polynomials over integers?

[tex]x^4 + 4[/tex]

[tex]x^4 + 3 ~x^2~y^2 + 2 ~y^4 + 4 ~x^2 + 5 ~y^2 + 3[/tex]

If not, the following free math tutoring videos can help:

https://www.youtube.com/watch?v=Q2221B7lESA&t=544s

https://www.youtube.com/watch?v=uNFArkngg-4&t=16s

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[tex]x^{4 }[/tex]+4= [ [tex](x^{2 }) ^{2 }+ (2)^{2 } +2.2. x^{2 } ] -2.2. x^{2 }[/tex]=

=[tex](x^{2 }+2) ^{2 } - (2x)^{2 }[/tex]= ([tex]x^{2 }[/tex]+2-2x)([tex]x^{2 }[/tex]+2+2x)
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[tex]x^{4 } +3x^{2 } y^{2 } +2y^{4 }+ x^{2 }+3 x^{2 } +2y^{2 }+ 3y^{2 }+3[/tex]=

=([tex]x^{4 } +2y^{4 }+ x^{2 } +2y^{2 }[/tex]) +3([tex]x^{2 } y^{2 }+ x^{2 } +y^{2 }+1) =[/tex]

= [tex][x^{2 }( x^{2 }+1) +2 y^{2 }( y^{2 }+1) ] +3[ x^{2 }( y^{2 }+1) +( y^{2 }+1) ]=[/tex]

= [tex]x^{2 }( x^{2 }+1)+2 y^{2 } (y^{2 }+1)+3 (y^{2 }+1)( x^{2 }+1)[/tex]=

=[tex]x^{2 }( x^{2 } +1)[/tex]+[tex]2y^{2 } (y^{2 }+1)[/tex]+[tex](y^{2 } +1)(x^{2 }+1)[/tex][tex]+2(y^{2 } +1)( x^{2 }+1)[/tex] =

=[tex](x^{2 }+1)( x^{2 } +y^{2 } +1)[/tex][tex]+2(y^{2 } +1)(x^{2 } +y^{2 } +1)[/tex]=

=[tex](x^{2 } +y^{2 }+1)( x^{2 } +1+2y^{2 } +2)=[/tex]

= [tex](x^{2 } +y^{2 } +1)(x^{2 } +2y^{2 }+3)[/tex]