Question

add the polynomials and find the sum of the expression.
Polynomials #1: -9m^3+15m^5-3m^2-14
Polynomials #2: 10-5m^2+8m-3m^5

The sum of the expression is:

Answer 1

To add the two polynomials, we will align like terms:

**Polynomials:**
1. \(-9m^3 + 15m^5 - 3m^2 - 14\)
2. \(10 - 5m^2 + 8m - 3m^5\)

Now, let's add them together step by step:

1. Combine the \(m^5\) terms:
\[
15m^5 - 3m^5 = 12m^5
\]

2. Combine the \(m^3\) terms:
\[
-9m^3 = -9m^3 \quad (\text{no other \(m^3\) term to combine with})
\]

3. Combine the \(m^2\) terms:
\[
-3m^2 - 5m^2 = -8m^2
\]

4. Combine the \(m\) terms:
\[
8m = 8m \quad (\text{no other \(m\) term to combine with})
\]

5. Combine the constant terms:
\[
-14 + 10 = -4
\]

Now, put it all together:

\[
12m^5 - 9m^3 - 8m^2 + 8m - 4
\]

Thus, the sum of the expression is:

\[
\boxed{12m^5 - 9m^3 - 8m^2 + 8m - 4}
\]