Question

add the polynomial expressions and fill the answer blanks
-3k + 4k^2 - 2 and 9k^2 - 3k^3 + 4k - 3
_k^3 + _k^2 + _k +_

Answer 1

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

1. Write both polynomials:

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

2. Rearrange and combine like terms:

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

This simplifies to:

\(-3k^3 + 13k^2 + k - 5\)

So, the result is:

\(-3k^3 + 13k^2 + 1k - 5\)

Now let’s fill in the blanks:

\(-3k^3 + 13k^2 + 1k - 5\)

Thus, the filled answer is:

\(-3\) for \(k^3\),
\(13\) for \(k^2\),
\(1\) for \(k\),
\(-5\) for the constant term.