Question

Разложите многочлен на множители

Answer 1

$y^3-6+11y-6y^2=y^3-6+11y-6y^2+y-y=\\\\(y^3-y)-(6-12y+6y^2)=\\\\(y*y^2-y*1)-(6*1-6*2y+6*y^2)=\\\\y(y^2-1)-6(1-2y+y^2)=\\\\y(y^2-1^2)-6(1^2-2*1*y+y^2)=\\\\y(y-1)(y+1)-6(y-1)^2=\\\\(y-1)(y^2+y)-(y-1)(6y-6)=\\\\(y-1)((y^2+y)-(6y-6))=\\\\(y-1)(y^2+y-6y+6)=\\\\(y-1)(y^2-5y+6)=\\\\(y-1)(y^2-2y-3y+6)=\\\\(y-1)((y^2-2y)-(3y-6))=\\\\(y-1)(y(y-2)-3(y-2))=\\\\(y-1)(y-2)(y-3)$
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$x^4-(a^2+1)x^2+a^2=x^4-x^2-a^2x^2+a^2=\\\\(x^4-x^2)-(a^2x^2-a^2)=\\\\x^2(x^2-1)-a^2(x^2-1)=\\\\(x^2-a^2)(x^2-1)=(x-a)(x+a)(x-1)(x+1)$