Question

add the polynomials 8m^4 - 17m^6 + 2m^3 - 18 and 12 + 6m^3 + 8m^6 - 13m^5

be sure to write the final answer in descending order. (The largest exponent to the smallest)

Answer 1

To add the polynomials \(8m^4 - 17m^6 + 2m^3 - 18\) and \(12 + 6m^3 + 8m^6 - 13m^5\), we will combine like terms.

Starting with the two polynomials:

1. \(8m^4 - 17m^6 + 2m^3 - 18\)
2. \(12 + 6m^3 + 8m^6 - 13m^5\)

Now, let's group the like terms together:

\[
-17m^6 + 8m^6 \quad (\text{Combine } m^6 \text{ terms})
\]
\[
-13m^5 \quad (\text{Only one } m^5 \text{ term})
\]
\[
8m^4 \quad (\text{Only one } m^4 \text{ term})
\]
\[
2m^3 + 6m^3 \quad (\text{Combine } m^3 \text{ terms})
\]
\[
-18 + 12 \quad (\text{Combine constant terms})
\]

Now, let’s do the calculations step by step:

1. \( -17m^6 + 8m^6 = -9m^6\)
2. \( -13m^5\)
3. \( 8m^4\)
4. \( 2m^3 + 6m^3 = 8m^3\)
5. \( -18 + 12 = -6\)

Now, we combine all the results:

\[
-9m^6 - 13m^5 + 8m^4 + 8m^3 - 6
\]

Writing this final polynomial in descending order gives us:

\[
-9m^6 - 13m^5 + 8m^4 + 8m^3 - 6
\]

Thus, the final answer is:

\[
\boxed{-9m^6 - 13m^5 + 8m^4 + 8m^3 - 6}
\]