Question

Which expression represents the polynomial x7+x4−8x3−2x−6x6 rewritten in descending order, using coefficients of 0 for any missing terms

x7−6x6+0x5+x4−8x3+0x2−2xx7−6x6+0x5+x4−8x3+0x2−2x  0 x5

+0 x2 −2x−8 x3 + x4 −6 x6 + x7 0 x5 +0 x2 −2x−8 x3 + x4 −6 x6 + x7   x7 −2x−6 x6 +0 x5 + x4 −8 x3 x7 −2x−6 x6 +0 x5 + x4 −8 x3   x7 + x4 −2x−6 x6 −8 x3 +0 x2 +0 x5 x7 + x4 −2x−6 x6 −8 x3 +0 x2 +0 x5   x7 + x4 −8 x3 −2x−6 x6 +0

Answer 1

The polynomial
`x^7-6x^6+0x^5+x^4-8x^3+0x^2-2x` is complete, starting from the highest power to the lowest, covering all the terms.

Explanation:

`x^7+x^4-8x^3-2x-6x^6`

To write the complete polynomial in descending order, we will first rearrange the expression starting with the term which has the highest power and then add the missing terms in it using 0 as the coefficient for x:

`x^7-6x^6+x^4-8x^3-2x`

Now add the missing terms to get the complete polynomial in a descending order:

`x^7-6x^6+0x^5+x^4-8x^3+0x^2-2x`

Answer 2

polynomial
`x^7+x^4-8x^3-2x-6x^6` rewritten in descending order

Descending order we write from the highest degree to lowest degree

Highest degree is 7

`x^7-6x^6 +x^4-8x^3-2x`

Now we fill the missing terms

x^5 is missing so we write
`0x^5`

x^2 is missing so we write
`0x^2`

There is no constant term so we put 0 at the end

`x^7-6x^6 +0x^5 +x^4 - 8x^3 +0x^2 -2x +0`