a: \(x^2+7x+6=x^2+x+6x+6\)
=x(x+1)+6(x+1)
=(x+1)(x+6)
b: \(3x^2-7x+2\)
\(=3x^2-6x-x+2\)
=3x(x-2)-(x-2)
=(x-2)(3x-1)
d: \(-2x^3+x^2+12\)
\(=-2x^3+4x^2-3x^2+12\)
\(=-2x^2\left(x-2\right)-3\left(x-2\right)\left(x+2\right)\)
\(=\left(x-2\right)\left[-2x^2-3\left(x+2\right)\right]\)
\(=-\left(x-2\right)\left(2x^2+3x+6\right)\)
e: \(4x^4+81\)
\(=4x^4+36x^2+81-36x^2\)
\(=\left(2x^2+9\right)^2-\left(6x\right)^2\)
\(=\left(2x^2+9-6x\right)\left(2x^2+9+6x\right)\)
f: \(\left(x-7\right)\left(x-5\right)\left(x-3\right)\left(x-1\right)-20\)
\(=\left(x-7\right)\left(x-1\right)\left(x-5\right)\left(x-3\right)-20\)
\(=\left(x^2-8x+7\right)\left(x^2-8x+15\right)-20\)
\(=\left(x^2-8x\right)^2+22\left(x^2-8x\right)+105-20\)
\(=\left(x^2-8x\right)^2+22\left(x^2-8x\right)+85\)
\(=\left(x^2-8x+5\right)\left(x^2-8x+17\right)\)
g: \(3x\left(3x+2\right)\left(3x+4\right)\left(3x+6\right)+7\)
\(=\left(9x^2+18x\right)\left(9x^2+12x+6x+8\right)+7\)
\(=\left(9x^2+18x\right)^2+8\left(9x^2+18x\right)+7\)
\(=\left(9x^2+18x+1\right)\left(9x^2+18x+7\right)\)
h: \(x^4+x^3+6x^2+5x+5\)
\(=x^4+x^3+x^2+5x^2+5x+5\)
\(=x^2\left(x^2+x+1\right)+5\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^2+5\right)\)
