\(A\left(x\right)=6x^4+6x^3-5x-17\)
\(B\left(x\right)=6x^4+6x^3-2x^2-5x-15\)
\(A\left(x\right)+B\left(x\right)=\left(6x^4+6x^3-5x-17\right)+\left(6x^4+6x^3-2x^2-5x-15\right)\)
\(=12x^4+12x^3-2x^2-10x-32\)
\(C\left(x\right)=A\left(x\right)-B\left(x\right)\)
\(=\left(6x^4+6x^3-5x-17\right)-\left(6x^4+6x^3-2x^2-5x-15\right)\)
\(=6x^4+6x^3-5x-17-6x^4-6x^3+2x^2+5x+15\)
\(=2x^2-2\)
\(=2\left(x-1\right)\left(x+1\right)\)