a: \(12x^2-72x+60\)
\(=12\left(x^2-6x+5\right)\)
\(=12\left(x^2-x-5x+5\right)\)
\(=12\left[x\left(x-1\right)-5\left(x-1\right)\right]\)
\(=12\left(x-1\right)\left(x-5\right)\)
b:
\(9x^2-21x-18\)
\(=3\cdot3x^2-3\cdot7x-3\cdot6\)
\(=3\left(3x^2-7x-6\right)\)
\(=3\left(3x^2-9x+2x-6\right)\)
\(=3\left(x-3\right)\left(3x+2\right)\)
c:
\(x^6y+4x^2y\)
\(=x^2y\cdot x^4+x^2y\cdot4\)
\(=x^2y\left(x^4+4\right)\)
\(=x^2y\left(x^4+4x^2+4-4x^2\right)\)
\(=x^2y\left[\left(x^2+2\right)^2-\left(2x\right)^2\right]\)
\(=x^2y\left(x^2+2+2x\right)\left(x^2+2-2x\right)\)
d: \(x^7y+x^5y+x^3y\)
\(=x^3y\cdot x^4+x^3y\cdot x^2+x^3y\cdot1\)
\(=x^3y\left(x^4+x^2+1\right)\)
\(=x^3y\left[\left(x^4+2x^2+1\right)-x^2\right]\)
\(=x^3y\left[\left(x^2+1\right)^2-x^2\right]\)
\(=x^3y\left(x^2+1-x\right)\left(x^2+1+x\right)\)
e: \(x^3+6x^2+3x-10\)
\(=x^3+5x^2+x^2+5x-2x-10\)
\(=x^2\left(x+5\right)+x\left(x+5\right)-2\left(x+5\right)\)
\(=\left(x+5\right)\left(x^2+x-2\right)\)
\(=\left(x+5\right)\left(x+2\right)\left(x-1\right)\)
f: \(x^3+3x^2-33x-35\)
\(=x^3+7x^2-4x^2-28x-5x-35\)
\(=x^2\left(x+7\right)-4x\left(x+7\right)-5\left(x+7\right)\)
\(=\left(x+7\right)\left(x^2-4x-5\right)=\left(x-5\right)\left(x+1\right)\left(x+7\right)\)
