# How do you write the polynomial 3x^2-8x- 12x^5- 5x3+ 2x^4- 6 in standard form?

Dec 4, 2016

$- 12 {x}^{5} + 2 {x}^{4} - 5 {x}^{3} + 3 {x}^{2} - 8 x - 6$

#### Explanation:

I am assuming the $3$ in the $- 5 x$ term should be an exponent.

$3 {x}^{2} - 8 x - 12 {x}^{5} - 5 {x}^{3} + 2 {x}^{4} - 6$

To write the polynomial in standard form, write it in order of decreasing exponents. I have highlighted the exponents in red.

$- 12 {x}^{\textcolor{red}{5}} + 2 {x}^{\textcolor{red}{4}} - 5 {x}^{\textcolor{red}{3}} + 3 {x}^{\textcolor{red}{2}} - 8 x - 6$

Note that the $8 x$ term has an exponent of $\textcolor{red}{1}$ ($8 {x}^{\textcolor{red}{1}}$), but the $\textcolor{red}{1}$ is not typically written.

And, even the $- 6$ term has an exponent. Recall that ${x}^{0} = 1$, so $- 6 = - 6 {x}^{\textcolor{red}{0}}$. So the constant term $- 6$ also follows the rule of writing the terms in order of decreasing exponents.