a) \(A=\left(x^2+x\right)^2+4x^2+4x-12=\left[\left(x^2+x\right)^2+4\left(x^2+x\right)+4\right]-16=\left(x^2+x+2\right)^2-16=\left(x^2+x+2-4\right)\left(x^2+x+2+4\right)=\left(x^2+x+-2\right)\left(x^2+x+6\right)\)
b) \(B=x\left(x+1\right)\left(x+2\right)\left(x+3\right)+1=\left(x^2+3x\right)\left(x^2+3x+2\right)+1=\left(x^2+3x\right)^2+2\left(x^2+3x\right)+1=\left(x^2+3x+1\right)^2\)
c) \(C=\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24=\left[\left(x^2+7x+10\right)+2\left(x^2+7x+10\right)+1\right]-25=\left(x^2+7x+11\right)^2-25=\left(x^2+x+10-5\right)\left(x^2+x+10+5\right)=\left(x^2+x+5\right)\left(x^2+x+15\right)\)
d) \(D=x^4+1024=\left(x^4+64x^2+1024\right)-64x^2=\left(x^2+32\right)^2-64x^2=\left(x^2-8x+32\right)\left(x^2+8x+32\right)\)
