Answer: \(\mathrm{p}(x)=(x-1)(x-5)(x+6)\).

By the remainder theorem, the remainder when \(\mathrm{p}(x)\) is divided by \(x+2\) is \(\mathrm{p}(-2)\).

The remainder is given as \(84\), so

\(\mathrm{p}(-2)=84.\)

Now

\(\mathrm{p}(-2)=(-2)^3+A(-2)+30.\)

Thus

\(-8-2A+30=84.\)

So

\(22-2A=84,\)

which gives

\(A=-31.\)

Therefore

\(\mathrm{p}(x)=x^3-31x+30.\)

Use the factor theorem to find a linear factor. Testing \(x=1\),

\(1^3-31(1)+30=0,\)

so \((x-1)\) is a factor. Dividing gives

\(x^3-31x+30=(x-1)(x^2+x-30).\)

Finally,

\(x^2+x-30=(x-5)(x+6).\)

Hence

\(\mathrm{p}(x)=(x-1)(x-5)(x+6).\)