Question

x⁴+2x³ -2x²+2x-3

Answer 1

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

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

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

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

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