a. \(3x^4+4x^2+1=\left(3x^2+1\right)\left(x^2+1\right)\)
b. \(x^4+3x^2-4=\left(x^2-1\right)\left(x^2+4\right)\)
c. \(4x^4-37x^2+9=\left(x^2-9\right)\left(4x^2-1\right)\)
d. \(\left(x^2+x\right)^2+4\left(x^2+x\right)-12=x^4+2x^3+x^2+4x^2+4x-12=x^4+2x^3+5x^2+4x-12=\left(x-1\right)\left(x^3+3x^2+8x+12\right)=\left(x-1\right)\left(x+2\right)\left(x^2-x+6\right)\)
e. \(x\left(x+4\right)\left(x+6\right)\left(x+10\right)+128=x^4+20x^3+124x^2+240x+128=\left(x^2+10x+8\right)\left(x^2+10x+16\right)\)