Question

x^4+2x^3-6x^2+2x+1

Answer 1

\(x^4+2x^3-6x^2+2x+1=x^3\left(x-1\right)+3x^2\left(x-1\right)-3x\left(x-1\right)-\left(x-1\right)=\left(x-1\right)\left(x^3+3x^2-3x-1\right)\)

Answer 2

x⁴+2x³-6x²+2x+1=(x-1)(x³+3x²-3x-1)=(x-1)[(x³-1)+(3x²-3x)]

= (x-1)[(x-1)(x²+x+1)+3x(x-1)]

= (x-1)²(x²+4x+1)

Answer 3

\(x^4+2x^3-6x^2+2x+1\)

\(=x^4-x^3+3x^3-3x^2-3x^2+3x-x+1\)

\(=\left(x-1\right)\left(x^3+3x^2-3x-1\right)\)

\(=\left(x-1\right)\left[\left(x-1\right)\left(x^2+x+1\right)+3x\left(x-1\right)\right]\)

\(=\left(x-1\right)^2\cdot\left(x^2+4x+1\right)\)