a, \(9x^2+6x-8\)
\(=\left(9x^2+6x+1\right)-9\)
\(=\left(3x+1\right)^2-3^2\)
\(=\left(3x+1-3\right).\left(3x+1+3\right)\)
\(=\left(3x-2\right).\left(3x+4\right)\)
b, \(x^7+x^2+1\)
\(=x^7+x^2+x+1-x\)
\(=\left(x^7-x\right)+\left(x^2+x+1\right)\)
\(=x.\left(x^6-1\right)+\left(x^2+x+1\right)\)
\(=x.\left(x^3-1\right).\left(x^3+1\right)+\left(x^2+x+1\right)\)
\(=x.\left(x-1\right).\left(x^2+x+1\right).\left(x^3-1\right)+\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right).\left[x.\left(x-1\right).\left(x^3+1\right)+1\right]\)
\(=\left(x^2+x+1\right).\left[\left(x^2-x\right).\left(x^3+1\right)+1\right]\)
\(=\left(x^2+x+1\right).\left(x^5+x^2-x^4-x+1\right)\)
\(=\left(x^2+x+1\right).\left(x^5-x^4+x^2-x+1\right)\)
c, \(x^5+x^4+1\)
\(=x^5+x^4+x^2+x+1-x^2-x\)
\(=\left(x^5-x^2\right)+\left(x^4-x\right)+\left(x^2+x+1\right)\)
\(=x^2.\left(x^3-1\right)+x.\left(x^3-1\right)+\left(x^2+x+1\right)\)
\(=x^2.\left(x-1\right).\left(x^2+x+1\right)+x.\left(x-1\right).\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right).\left[x^2.\left(x-1\right)+x.\left(x-1\right)+1\right]\)
\(=\left(x^2+x+1\right).\left(x^3-x+x^2-x+1\right)\)
\(=\left(x^2+x+1\right).\left(x^3-x+1\right)\)
a) \(9x^2+6x-8\Leftrightarrow9x^2+12x-6x-8\Leftrightarrow3x\left(3x+4\right)-2\left(3x+4\right)\)
\(\Leftrightarrow\left(3x-2\right)\left(3x+4\right)\)
