Question

c) (x^2 + x + 1) (x^2 + x + 2) - 12

Answer 1

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

Đặt \(y=x^2+x+1\)

\(\left(1\right)=y\left(y+1\right)-12\)

      \(=y^2+y-12\)

      \(=y^2-3y+4y-12\)

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

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

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

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

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

 

Answer 2

Đặt \(t=x^2+x+1\) thì \(\left(x^2+x+1\right)\left(x^2+x+2\right)-12=t\left(t+1\right)-12=t^2+t-12=\left(t-3\right)\left(t+4\right)\)

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