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x^4+x^2+1 = (x^4+2x^2+1)-x^2 = (x^2+1)^2-x^2 = (x^2-x+1).(x^2+x+1)
k mk nha
x5-x4-1=x5-x3-x2-x4+x2+x+x3-x-1
=x2.(x3-x-1)-x.(x3-x-1)+(x3-x-1)
=(x3-x-1)(x2-x+1)
x^4+x^2+1 = (x^4+2x^2+1)-x^2 = (x^2+1)^2-x^2 = (x^2-x+1).(x^2+x+1)
k mk nha
\(x^4+1\)
\(=x^4+2x^2+1-2x^2\)
\(=\left(x^2+1\right)^2-2x^2\)
\(=\left(x^2-\sqrt{2}x+1\right)\left(x^2+\sqrt{2}x+1\right)\)
\(x^8+x^4+1\)
\(=x^4.\left(x^4+1\right)+\left(x^4+1\right)-x^4\)
\(=\left(x^4+1\right).\left(x^4+1\right)-\left(x^2\right)^2\)
\(=\left(x^4+1\right)^2-\left(x^2\right)^2\)
\(=\left(x^4+1-x^2\right).\left(x^4+1+x^2\right)\)
x^8 + 4 = x^8 + 4x^4 + 4 - 4 x^4
= ( x^ 4 + 2 )^2 - (2x^2)^2
= ( x^4 + 2x^2 + 2 )( x^4 - 2x^2 + 2)
\(x^4+81\)
\(=x^4+3^4\)
\(=\left(x^2+3^2\right)^2-2x^23^2\)
\(=\left(x^2+\sqrt{2}x3+3^2\right)\left(x^2-\sqrt{2}x3+3^2\right)\)
nguồn gg
\(x^4+81\)
\(=x^4+18x^2+81-18x^2\)
\(=\left(x^2+9\right)^2-18x^2\)
\(=\left(x^2-3\sqrt{2}x+9\right)\left(x^2+3\sqrt{2}x+9\right)\)
x4y4 + 4
= x4y4 + 4x2y2 + 4 - 4x2y2
= (x2y2 + 2)2 - (2xy)2
= (x2y2 - 2xy + 2)(x2y2 + 2xy + 2)
x4y4 + 64
= x4y4 + 16x2y2 + 64 - 16x2y2
= (x2y2 + 8)2 - (4xy)2
= (x2y2 - 4xy + 8)(x2y2 + 4xy + 8)
x5 + x + 1
= x5 - x2 + x2 + x + 1
= x2(x3 - 1) + (x2 + x + 1)
= x2(x - 1)(x2 + x + 1) + (x2 + x + 1)
= (x2 + x + 1)[x2(x - 1) + 1]
x^6 +4= ( x^3 ) ^2 + 4x^3 + 4 - 4x^3
= ( x^3 + 2 )^2 - 4x^3
\(x^6+4\)
\(=\left(x^3\right)^2+2x.2+2^2-2^2+4\)
\(=\left(x^3+2\right)^2-\left(2x\right)^2\)
\(=\left(x^3+2-2x\right).\left(x^3+2+2x\right)\)