\(x^3+8x^2+17x+10=x^3+x^2+7x^2+7x+10x+10\)
\(=x^2\left(x+1\right)+7x\left(x+1\right)+10\left(x+1\right)=\left(x+1\right)\left(x^2+7x+10\right)\)
\(=\left(x+1\right)\left(x^2+2x+5x+10\right)=\left(x+1\right)\left[x\left(x+2\right)+5\left(x+2\right)\right]=\left(x+1\right)\left(x+2\right)\left(x+5\right)\)