5(x^2+3)^4(2x)(x-2)^4+(x^2+3)^5(4)(x-2)^3

I'll just factorise it.   

$$\\5(x^2+3)^4(2x)(x-2)^4+(x^2+3)^5(4)(x-2)^3\\\\
10x(x^2+3)^4(x-2)^4+4(x^2+3)^5(x-2)^3\\\\
2(x-2)^3(x^2+3)^4\;\;[5x(x-2)+2(x^2+3)]\\\\
2(x-2)^3(x^2+3)^4\;\;[5x^2-10x+2x^2+6]\\\\
2(x-2)^3(x^2+3)^4\;\;[7x^2-10x+6]\\\\$$