\(a,6x^4-11x^2+5\\ =\left(6x^4-6x^2\right)+\left(-5x^2+5\right)\\ =6x^2\left(x^2-1\right)-5\left(x^2-1\right)\\ =\left(6x^2-5\right)\left(x^2-1\right)\\ =\left(6x^2-5\right)\left(x-1\right)\left(x+1\right)\\ b,\left(x^2-2x\right)^2+4\left(x^2-2x\right)-12\\ =\left[\left(x^2-2x\right)^2-2\left(x^2-2x\right)\right]+\left[6\left(x^2-2x\right)-12\right]\\ =\left(x^2-2x\right)\left(x^2-2x-2\right)+6\left(x^2-2x-2\right)\\ =\left(x^2-2x-2\right)\left(x^2-2x+6\right)\\ e,\left(x^2+2x\right)^2+9x^2+18x+20\\ =\left(x^2+2x\right)^2+9\left(x^2+2x\right)+20\\ =\left[\left(x^2+2x\right)^2+4\left(x^2+2x\right)\right]+\left[5\left(x^2+2x\right)+20\right]\\ =\left(x^2+2x\right)\left(x^2+2x+4\right)+5\left(x^2+2x+4\right)\\ =\left(x^2+2x+4\right)\left(x^2+2x+5\right)\)
\(d,\left(x^2+3x+1\right)\left(x^2+3x+2\right)-6\\ =\left(x^2+3x+1\right)\left[\left(x^2+3x+1\right)+1\right]-6\\ =\left(x^2+3x+1\right)^2+\left(x^2+3x+1\right)-6\\ =\left[\left(x^2+3x+1\right)^2-2\left(x^2+3x+1\right)\right]+\left[3\left(x^2+3x+1\right)-6\right]\\ =\left(x^2+3x+1\right)\left(x^2+3x+1-2\right)+3\left(x^2+3x+1-2\right)\\ =\left(x^2+3x+1\right)\left(x^2+3x-1\right)+3\left(x^2+3x-1\right)\\ =\left(x^2+3x-1\right)\left(x^2+3x+1+3\right)\\ =\left(x^2+3x-4\right)\left(x^2+3x+4\right)\\ e,\left(x^2+6x+5\right)\left(x+2\right)\left(x+4\right)-28\\ =\left(x^2+6x+5\right)\left(x^2+6x+8\right)-28\\ =\left(x^2+6x\right)^2+5\left(x^2+6x\right)+8\left(x^2+6x\right)+40-28\\ =\left(x^2+6x\right)^2+13\left(x^2+6x\right)+12\\ =\left[\left(x^2+6x\right)^2+\left(x^2+6x\right)\right]+\left[12\left(x^2+6x\right)+12\right]\\ =\left(x^2+6x\right)\left(x^2+6x+1\right)+12\left(x^2+6x+1\right)\\ =\left(x^2+6x+1\right)\left(x^2+6x+12\right)\)
