Question

разложите множители на многочлена
a^2-ab-8a+8b
x^3+3x^2+3x+9
x^3+x^2y-x^2z-xyz
m^2x^4-mnx^3+2mx^2-2nx-n+mx

Answer 1

$a^2-ab-8a+8b=a(a-b)-8(a-b)=(a-b)(a-8)\\\\\\x^3+3x^2+3x+9=x^2(x+3)+3(x+3)=(x+3)(x^2+3)\\\\\\x^3+x^2y-x^2z-xyz=x^2(x+y)-xz(x+y)=(x+y)(x^2-xz)=\\=x\, (x+y)(x-z)$

$m^2x^4-mnx^3+2mx^2-2nx-n+mx=\\\\mx^3(mx-n)+2x(mx-n)+(mx-n)=(mx-n)(mx^3+2x+1)$