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Kylibyaka
@Kylibyaka
June 2022
1
23
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Разложить многочлены на множители
44 балла
x^3+x^2-x-1
a^2-b^2-a-b
m^5-m^3+m^2-1
x-y-x^2+y^2
x^4-x^3+x-1
Заранее спасибо
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Flash3146
X^3+x^2-x-1=(x³+x²)+(-x-1)=x²(x+1)-1(x+1)=
(x+1)(x²-1)
a^2-b^2-a-b=(a²-b²)+(-a-b)=(a-b)(a+b)-1(a+b)=(a+b)(a-b)-1))
m^5-m^3+m^2-1=(m^5+m²)+(-m³-1)=
m²(m³+1)-1(m³+1)=(m³+1)(m²-1)
x-y-x^2+y^2=(x-y)+(-x²+y²)=(x-y)+(y²-x²)=
(x-y)+(y-x)(y+x)=(x-y)-(-y+x)(y+x)=(x-y)(-y-x)
x^4-x^3+x-1=(x⁴-x³)+(x-1)=x³(x-1)+1(x-1)=(x-1)(x³+1)
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Answers & Comments
(x+1)(x²-1)
a^2-b^2-a-b=(a²-b²)+(-a-b)=(a-b)(a+b)-1(a+b)=(a+b)(a-b)-1))
m^5-m^3+m^2-1=(m^5+m²)+(-m³-1)=
m²(m³+1)-1(m³+1)=(m³+1)(m²-1)
x-y-x^2+y^2=(x-y)+(-x²+y²)=(x-y)+(y²-x²)=
(x-y)+(y-x)(y+x)=(x-y)-(-y+x)(y+x)=(x-y)(-y-x)
x^4-x^3+x-1=(x⁴-x³)+(x-1)=x³(x-1)+1(x-1)=(x-1)(x³+1)