Question

( x^2 + x + 1 ) ( x^2 +x + 2)  -12

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Answer 1

\(\left(x^2+x+1\right)\left(x^2+x+2\right)-12\)

\(=t\left(t+1\right)-12\)( Đặt \(t=x^2+x+1\))

\(=t^2+t-12\)

\(=t^2-3t+4t-12\)

\(=t\left(t-3\right)+4\left(t-3\right)\)

\(=\left(t-3\right)\left(t+4\right)\)

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

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

\(=\left(x^2-1x+2x-2\right)\left(x^2+x+5\right)\)

\(=\left[x\left(x-1\right)+2\left(x-1\right)\right]\left(x^2+x+5\right)\)

\(=\left(x+2\right)\left(x-1\right)\left(x^2+x+5\right)\)