Question 119638
I am assuming you mean
Divide:  {{{(4x^4 - 12x^3 - 48x - 60)}}} by {{{(x - 4)}}}

If so, then we start by asking what quantity multiplied by {{{x}}} results in {{{4x^4}}} which we can see is {{{4x^3}}}. We then multiply {{{-4}}} by {{{4x^3}}} to get {{{-16x^3}}} and subtract from {{{-12x^3}}} which gives us {{{4x^3}}}.

So now we want to know what {{{4x^3 + 0 x^2 - 48x - 60}}} divided by {{{x - 4}}} is. We start as in the first step and ask what quantity multiplied by x gives us {{{4x^3}}}. The answer to this question is {{{4x^2}}}. Multiplying {{{-4}}} by {{{4x^2}}} results in {{{-16x^2}}}. Subtracting {{{-16x^2}}} from {{{0x^2}}} leaves us with {{{16x^2}}}.

The next division is {{{16x^2 - 48x - 60}}} by {{{x - 4}}}. As we have done previously, we ask what we need to multiply {{{x}}} by to get {{{16x^2}}} and find that the quantity would be {{{16x}}}. Multiplying {{{16x}}} by {{{-4}}} gives us {{{-64x}}} and subtracting from {{{-48x}}} gives us {{{16x}}}.

Finally, we want to know what {{{16x - 60}}} divided by {{{x - 4}}} is. We see that {{{16x}}} divided by {{{x}}} is {{{16}}} and multiplying {{{-4}}} by {{{16}}} results in {{{-64}}}. Subtracting {{{-64}}} from {{{-60}}} gives us a remainder of {{{4}}}.

Thus {{{(4x^4 - 12x^3 - 48x - 60)}}} divided by {{{(x - 4) = 4x^3+4x^2+16x+16 + 4/(x-4)}}}.