# How do you write 3x^4+2x^3-5-x^4 in standard form?

$2 {x}^{4} + 2 {x}^{3} - 5$
The standard form of a polynomial (which is what we have here) is written from highest exponent to lowest exponent. In addition, there should only be 1 of each exponent/variable pair (like x^4 or x^3). For example, here we have $3 {x}^{4}$ and $- {x}^{4}$; but we can only have 1 term with an ${x}^{4}$ in it. To fix this, we need to combine these terms by adding $3 {x}^{4}$ to $- {x}^{4}$; the result is $2 {x}^{4}$ (remember that $3 {x}^{4} + \left(- {x}^{4}\right)$ is the same thing as $3 {x}^{4} - {x}^{4}$).
From here, we just need to organize a bit - from highest exponent to lowest. Our highest is, of course, $4$. Then we have $3$ - and since we don't have ${x}^{2}$ or $x$, we ignore them. Now, what about the $- 5$? Well, since ${x}^{0} = 1$, we can write $- 5$ as $- 5 {x}^{0}$, which is the same thing as $- 5 \cdot 1$ - which equals $- 5$. That makes 0 our lowest exponent. Cool, huh?
Finally, we simply write it. We start with the term with the highest exponent ($2 {x}^{4}$), and then go down from there. So, our polynomial in standard form is $2 {x}^{4} + 2 {x}^{3} - 5$. And we're done.