15) \(x^3-3x^2+3x+7\)
\(=x^3-3x^2+3x-1+8\)
\(=\left(x^3-3x^2+3x-1\right)+2^3\)
\(=\left(x-1\right)^3+2^3\)
\(=\left[\left(x-1\right)+2\right]\left[\left(x-1\right)^2-2\left(x-1\right)+2^2\right]\)
\(=\left(x+1\right)\left(x^2-2x+1-2x+2+4\right)\)
\(=\left(x+1\right)\left(x^2-4x+7\right)\)
16) \(2x^3-3x^2+3x-1\)
\(=x^3+x^3-3x^2+3x-1\)
\(=x^3+\left(x^3-3x^2+3x-1\right)\)
\(=x^3+\left(x-1\right)^3\)
\(=\left[x+\left(x-1\right)\right]\left[x^2-x\left(x-1\right)+\left(x-1\right)^2\right]\)
\(=\left(2x-1\right)\left(x^2-x^2+x+x^2-2x+1\right)\)
\(=\left(2x-1\right)\left(x^2-x+1\right)\)
\(a,x^3-3x^2+3x+7\\ =x^3+x^2-4x^2-4x+7x+7\\ =x^2\left(x+1\right)-4x\left(x+1\right)+7\left(x+1\right)\\ =\left(x+1\right)\left(x^2-4x+7\right)\\ b,2x^3-3x^2+3x-1\\ =2x^3-x^2-2x^2+x+2x-1\\ =x^2\left(2x-1\right)-x\left(2x-1\right)+\left(2x-1\right)\\ =\left(2x-1\right)\left(x^2-x+1\right)\)
