Question

Which of the following shows 8x3y + x2 − 14z − 2 + 5y2x written in standard form?

Answer 1

Is this what you're referring to?
\[\large 8x^3y+x^2-14z-2+5y^2x\]

Answer 2

Standard form is usually something like this:
\[\large Ax+By=C \]
where A, B, and C are constants. But in your case, it might be a little more like:
\[\large Ax+By+Cz=D\]
with A, B, C, and D still being some constant.

Answer 3

You want to arrange it in a way where x is the leading coefficient and also where it is the highest power. Then followed by "y" and "z" and so on. You can start by turning it into an equation:
\[\large 8x^3y+x^2-14z-2+5y^2x = 0\]
Observe how x^3 is the highest power in the equation, so that would be the leading coefficient in the equation:
\[\large \color{green}{8x^3y} +x^2-14z-2+5y^2x=0 \]
Usually you would look for the next variable with a third power, but since there are none, you would just move on to the next power of 2 and put that next, with x still being the leading variable, then y, and then z if it's there:
\[\large \color{green}{8x^3y} +\color{red}{x^2}-14z-2+\color{red}{5y^2x}=0 \]
They would follow the leading term and be:
\[\large 8x^3y+x^2+5y^2x-14z-2=0\]

Just move the constant "-2" to the other side of the equation and you should be set.