a. \(x^3+4x^2-31x-70=x^3+2x^2+2x^2+4x-35x-70=\left(x^3+2x^2\right)+\left(2x^2+4x\right)-\left(35x+70\right)=x^2\left(x+2\right)+2x\left(x+2\right)-35\left(x+2\right)=\left(x+2\right)\left(x^2+2x-35\right)=\left(x+2\right)\left(x^2+7x-5x-35\right)=\left(x+2\right)[\left(x^2+7x\right)-\left(5x+35\right)]=\left(x+2\right)\left[x\left(x+7\right)-5\left(x+7\right)\right]=\left(x+2\right)\left(x+7\right)\left(x-5\right)\)
b. \(y^2-y-12=y^2-4y+3y-12=\left(y^2+3y\right)-\left(4y+12\right)=y\left(y+3\right)-4\left(x+3\right)=\left(x+3\right)\left(y-4\right)\)
c. \(x^2-3x^2+4x-2=-2x^2+4x-2=-2\left(x^2-2x+1\right)=-2\left(x-1\right)^2\)
