$h\left(x\right)=a\left(\left(a+1\right)x^6-x^5+x^4+2\right)+\left(a-3\right)x^6+a{x}^5+2x^4-1=$

$=\left(a^2+a\right)x^6-a{x}^5+a{x}^4+2a+\left(a-3\right)x^6+a{x}^5+2x^4-1=$

$=\left(a^2+a+a-3\right)x^6+\left(a+2\right)x^4+\left(2a-1\right)=$