Question

add the polynomial expressions
-3k + 4k^2 - 2 and 9k^2 - 3k^3 + 4k - 3

Answer 1

To add the polynomial expressions \(-3k + 4k^2 - 2\) and \(9k^2 - 3k^3 + 4k - 3\), we will combine like terms.

**Step 1: Write the expressions together:**

\[
(-3k + 4k^2 - 2) + (9k^2 - 3k^3 + 4k - 3)
\]

**Step 2: Rearranging the terms:**

\[
-3k + 4k^2 - 2 + 9k^2 - 3k^3 + 4k - 3
\]

**Step 3: Group the like terms:**

- \(k^3\) terms: \(-3k^3\)
- \(k^2\) terms: \(4k^2 + 9k^2 = 13k^2\)
- \(k\) terms: \(-3k + 4k = k\)
- Constant terms: \(-2 - 3 = -5\)

**Step 4: Combine these results:**

Putting it all together, we get:

\[
-3k^3 + 13k^2 + k - 5
\]

So, the sum of the polynomial expressions is:

\[
\boxed{-3k^3 + 13k^2 + k - 5}
\]