Question

Add the polynomial expressions 3−2p−5p^2 and p^4−3p+4 .(1 point)

Answer 1

To add the polynomial expressions \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), you simply combine like terms.

First, let's write the polynomials clearly:

1. \(3 - 2p - 5p^2\)
2. \(p^4 - 3p + 4\)

Now, we can rearrange and add the corresponding terms:

\[
p^4 + (-5p^2) + (-2p - 3p) + (3 + 4)
\]

Combining the like terms:

- The \(p^4\) term: \(p^4\)
- The \(p^2\) term: \(-5p^2\)
- The \(p\) terms: \(-2p - 3p = -5p\)
- The constant terms: \(3 + 4 = 7\)

Putting it all together, we get:

\[
p^4 - 5p^2 - 5p + 7
\]

So, the sum of the two polynomial expressions is:

\[
p^4 - 5p^2 - 5p + 7
\]