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\(=\left(x^6+2x^5+x^4\right)-2\left(x^5+2x^4+x^3\right)+2\left(x^4+2x^3+x^2\right)\)
\(=x^2\left(x^2+x\right)^2-2x\left(x^2+x\right)^2+2\left(x^2+x\right)^2\)
\(=\left(x^2+x\right)^2\left(x^2-2x+2\right)\)
\(=x^2\left(x+1\right)^2\left(x^2-2x+2\right)\)
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\(x^4+6x^3+11x^2+6x+1\)
\(=x^4+3x^3+x^2+3x^3+9x^2+3x+x^2+3x+1\)
\(=\left(x^2+3x+1\right)^2\)
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\(x^4+6x^3+7x^2-6x+1\)
\(=x^4-2x^2+1+6x^3+9x^2-6x\)
\(=\left(x^2-1\right)^2+6x\left(x^2-1\right)+9x^2\)
\(=\left(x^2+3x-1\right)^2\)
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\(=\left(x^4+x^3+x^2\right)+\left(x^2+x+1\right)\)
\(=x^2\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^2+1\right)\left(x^2+x+1\right)\)
\(x^4+x^3+2x^2+x+1\)
\(=x^4+x^3+x^2+x^2+x+1\)
\(=\left(x^2+x+1\right)\left(x^2+1\right)\)
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a: Ta có: \(a^5-ax^4+a^4x-x^5\)
\(=a\left(a^4-x^4\right)+x\left(a^4-x^4\right)\)
\(=\left(a-x\right)\left(a+x\right)\left(a^2+x^2\right)\cdot\left(a+x\right)\)
\(=\left(a-x\right)\cdot\left(a+x\right)^2\cdot\left(a^2+x^2\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(x^2+6x-1\right)^2+2x^2+x^4+2\left(x^2+6x-1\right)\left(x^2+1\right)\)
\(\left(x^2+6x-1\right)^2+2\left(x^2+6x-1\right)\left(x^2+1\right)+\left(x^2+1\right)^2-1=\left(x^2+6x-1+x^2+1\right)^2-1=\left(2x^2+6x\right)^2-1=\left(2x^2+6x-1\right)\left(2x^2+6x+1\right)\)
\(\left(x^2+6x-1\right)^2+2\left(x^2+6x-1\right)\left(x^2+1\right)+x^4+2x^2\)
\(=\left(x^2+6x-1\right)\left(x^2+6x-1+2x^2+2\right)+x^4+2x^2\)
\(=\left(x^2+6x-1\right)\left(3x^2+6x+1\right)+x^4+2x^2\)
\(=\left(2x^2+6x-1\right)\left(2x^2+6x+1\right)\)
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\(2x^2+x-6\)
\(=2x^2-3x+4x-6\)
\(=x\left(2x-3\right)+2\left(2x-3\right)\)
\(=\left(2x-3\right)\left(x+2\right)\)
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\(6x^2-13x+6\)
\(=6x^2-9x-4x+6\)
\(=\left(2x-3\right)\left(3x-2\right)\)
x5-x4-30x3=x3(x2-x-30) = x3(x-6)(x+5)
\(x^5-x^4-30x^3=x^3\left(x^2-x-30\right)=x^3\left(x-6\right)\left(x+5\right)\)