\(C=\left(x^2+x+1\right)\left(x^2+x+2\right)-12\)
Đặt \(x^2+x+1=t\)
Ta được:
\(C=t\left(t+1\right)-12\)
\(C=t^2+t-12\)
\(C=t^2+4t-3t-12\)
\(C=t\left(t+4\right)-3\left(t+4\right)\)
\(C=\left(t+4\right)\left(x-3\right)\)
\(C=\left(x^2+x+5\right)\left(x^2+x-2\right)\)
\(C=\left(x^2+x+5\right)\left(x^2-x+2x-2\right)\)
\(C=\left(x^2+x+5\right)\left[x\left(x-1\right)+2\left(x-1\right)\right]\)
\(C=\left(x^2+x+5\right)\left(x-1\right)\left(x+2\right)\)
Vậy....
\(\left(x^2+x\right)^2+9x^2+9x+14\)
\(=x^4+2x^3+10x^2+9x+14\)
\(=x^4+x^3+2x^2+x^3+x^2+2x+7x^2+7x+14\)
\(=x^2\left(x^2+x+2\right)+x\left(x^2+x+2\right)+7\left(x^2+x+2\right) \)
\(=\left(x^2+x+2\right)\left(x^2+x+7\right)\)
(x2 + x)2 + 9x2 + 9x + 14
= (x2 + x)2 + 9(x2 + x) + 14
= (x2 + x)(x2 + x + 9) + 14
\(2x^3-35x+75\)
\(=2x^3+10x^2-10x^2-50x+15x+75\)
\(=2x^2\left(x+5\right)-10x\left(x+5\right)+15\left(x+5\right)\)
\(=\left(x+5\right)\left(2x^2-10x+15\right)\)
