Question

x⁶ - x⁴ + 2x³ + 2x²

Answer 1

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

\(=\left(x^6+2x^5+x^4\right)-\left(2x^5+4x^4+2x^3\right)+2\left(x^4+2x^3+x^2\right)\)

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

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

Answer 2

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

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

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

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

Answer 3

x^6+x^4+2x^3+2x^2

=x^2.(x^3+x^2)+2.(x^3+x^2)

=(x^2+2).(x^3+x^2)

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