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\(x^5+x^4-x^3+x^2-x+2\)
\(=x^5-x^4+x^3-x^2+x+2x^4-2x^3+2x^2-2x+2\)
\(=x\left(x^4-x^3+x^2-x+1\right)+2\left(x^4-x^3+x^2-x+1\right)\)
\(=\left(x+2\right)\left(x^4-x^3+x^2-x+1\right)\)
f) \(x^2-6x+5=\left(x^2-x\right)+\left(-5x+5\right)=x\left(x-1\right)-5\left(x-1\right)=\left(x-1\right)\left(x-5\right)\)
g) \(x^4+64=\left(x^2+4x+8\right)\left(x^2-4x+8\right)\)
\(x^2-6x+5\)
\(=\left(x^2-2.3x+3^2\right)-4\)
\(=\left(x-3\right)^2-2^2\)
\(=\left(x-3-2\right)\left(x-3+2\right)\)
\(=\left(x-5\right)\left(x-1\right)\)
\(x^8+x^4+1\)
\(=x^8+x^7+x^6-x^7-x^6-x^5+x^5+x^4+x^3-x^3-x^2-x+x^2+x+1\)
\(=\left(x^8+x^7+x^6\right)-\left(x^7+x^6+x^5\right)+\left(x^5+x^4+x^3\right)-\left(x^3+x^2+x\right)+\left(x^2+x+1\right)\)
\(=x^6\left(x^2+x+1\right)-x^5\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)-x\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^6-x^5+x^3-x+1\right)\)
\(x^5-x^4-1\)
\(=x^5-x^4+x^3-x^3+x^2-x-x^2+x-1\)
\(=\left(x^5-x^4+x^3\right)-\left(x^3-x^2+x\right)-\left(x^2-x+1\right)\)
\(=x^3\left(x^2-x+1\right)-x\left(x^2-x+1\right)-\left(x^2-x+1\right)\)
\(=\left(x^2-x+1\right)\left(x^3-x-1\right)\)
\(x^5+x^4+2\)
\(=x^5+x^4+x^2-x^2+1+1\)
\(=\left(x^5-x^2\right)+\left(x^4+x^2+1\right)\)
\(=\left(x^5-x^2\right)+\left(x^4+2x^2-x^2+1\right)+1\)
\(=x^2\left(x^3-1\right)+\left(x^4+2x^2-x^2+1\right)+1\)
\(=x^2\left(x-1\right)\left(x^2+x+1\right)+\left(\left(x^2+1\right)^2-x^2\right)+1\)
\(=x^2\left(x-1\right)\left(x^2+x+1\right)+\left(x^2+1+x\right)\cdot\left(x^2+1-x\right)+1\)
\(=\left(x^3-x^2\right)\left(x^2+x+1\right)+\left(x^2+1+x\right)\cdot\left(x^2+1-x\right)+1\)
\(=\left(x^2+x+1\right)\left(x^3-x^2+x^2+1-x\right)+1\)
\(=\left(x^2+x+1\right)\left(x^3+1-x\right)+1\)
\(x^5+x+1\)
\(\Leftrightarrow\left(x^5+x^4+x^3\right)-\left(x^4+x^3+x^2\right)+\left(x^2+x+1\right)\)
\(\Leftrightarrow x^3\left(x^2+x+1\right)-x^2\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(\Leftrightarrow\left(x^2+x+1\right)\left(x^3-x^2+1\right)\)
Tk nka !!
\(x^5+x+1=x^5-x^2+x^2+x+1\)
\(=x^2\left(x^3-1\right)+x^2+x+1\)
\(=x^2\left(x-1\right)\left(x^2+x+1\right)+x^2+x+1\)
\(=\left(x^3-x^2+1\right)\left(x^2+x+1\right)\)
x5 + x4 + 1 = x5 - x3 - x2 - x4 + x2 + x + x3 - x - 1
= x2 ( x3 - x - 1 ) - x ( x3 - x - 1 ) + 1 ( x3 - x - 1 )
= ( x3 - x - 1 ) ( x2 - x + 1 )
x5+x4+1
= x5+x2-x2+x4-x+x+1
=x2(x3-1) + (x3+1) +x2+x+1
= x2(x-1)(x2+x+1)+x(x-1)( x2+x+1) +x2+x+1
=( x2 + x+1)( x3-x2+x2-x+1)
=(x2 + x+1)( x3-x+1)