Question

x^4+2x^3+3x^2+2x+1

Answer 1

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

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

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

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

Answer 2

x^4+2x^3+3x^2+2x+1

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

= x\(^2\) ( x\(^2\) + x + 1) + x ( x\(^2\) + x +1 ) + ( x\(^2\) + x + 1 )

= ( x\(^2\) + x + 1 ) ( x\(^2\) + x + 1 )

= ( x\(^2\) + x + 1 )\(^2\)