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x^5+x^4+1=x^5+x^4+x^3-x^3-x^2-x+x^2+x+1=x^3(x^2+x+1)-x(x^2+x+1)+x^2+x+1=(x^3-x+1)(x^2+x+1)
\(x^5+x^4+1\)
\(=x^3\left(x^2+x+1\right)-x\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^3-x+1\right)\left(x^2+x+1\right)\)
Ta có : x5 - x4 + x4 - x3 - x4 + x3 - x2 + x2 - x + x - 1
= x4(x - 1) + x3(x - 1) - x3(x - 1) - x2(x - 1) + x2(x - 1) + (x - 1)
= (x4 + x3 - x3 - x2 + x2 + 1) (x - 1)
= (x4 + 1)(x - 1)
Ta có:
\(x^5+x^4+1\)
\(=x^5+x^4+x^3+1-x^3\)
\(=\left(x^5+x^4+x^3\right)+\left(1^3-x^3\right)\)
\(=x^3\left(x^2+x+1\right)+\left(1-x\right)\left(1+x+x^2\right)\)
\(=\left(x^2+x+1\right)\left(x^3+1-x\right)\)
\(a^5+a^4+1=a^5+a^4+a^3-a^3+a^2-a^2+a-a+1\)
\(=a^5+a^4+a^3-a^3-a^2-a+a^2+a+1\)
\(=\left(a^5+a^4+a^3\right)-\left(a^3+a^2+a\right)-\left(a^2+a+1\right)\)
\(=a^3\left(a^2+a+1\right)-a\left(a^2+a+1\right)+\left(a^2+a+1\right)\)
\(=\left(a^2+a+1\right)\left(a^3-a+1\right)\)
#by_Suho
= x^10 - x + x^5 - x^2 + x^2 + x + 1
= x ( x^9 - 1 ) + x^2 (x^3 - 1 ) + x^2 + x + 1
= x [ ( x^3 - 1) ( x^6 + x^3 + 1 )] + x^2 ( x - 1 )(x^2 + x + 1 ) + x^2 + x + 1
= x ( x - 1 )(x^2 + x + 1 )(x^6 + x^3 + 1) + x^2 (x-1 )(x^2 + x+ 1 ) + x^2 + x + 1
= (x^2 + x + 1 )[ x(x-1)(x^6 + x^3 + 1 ) + x^2 + 1 )
Nhân ra giúp mình nha
x10 + x5 + 1 = (x10 - x) + (x5 - x2) + (x2 + x + 1) = x.[(x3)3 - 1] + x2.(x3 - 1) + (x2 + x + 1)
= x.(x3 - 1).(x6 + x3 + 1) + x2.(x3 - 1) + (x2 + x + 1)
= (x2 + x + 1). [x.(x -1).(x6 + x3 + 1) + x2 + 1 ]
x5 + x4 + 1
= x5 + x4 + x3 - x3 + 1
= x3(x2 + x + 1) - (x3 - 1)
= x3(x2 + x + 1) - (x - 1)(x2 + x + 1)
= (x3 - x + 1)(x2 + x + 1)