Question

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

Answer 1

`-12x^5+2x^4-5x^3+3x^2-8x-6`

Explanation:

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

`3x^2-8x-12x^5-5x^3+2x^4-6`

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

`-12x^color(red)5+2x^color(red)4-5x^color(red)3+3x^color(red)2-8x-6`

Note that the `8x` term has an exponent of `color(red)1` (`8x^color(red)1`), but the `color(red)1` is not typically written.

And, even the `-6` term has an exponent. Recall that `x^0=1`, so `-6=-6x^color(red)0`. So the constant term `-6` also follows the rule of writing the terms in order of decreasing exponents.