Question

Add the polynomial expressions 3−2p−5p2 and p4−3p+4 .

Answer 1

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

The first polynomial is:
\[ -5p^2 - 2p + 3 \]

The second polynomial is:
\[ p^4 - 3p + 4 \]

Now we will write them together and add the corresponding terms:

1. \(p^4\) (from the second polynomial)
2. \(-5p^2\) (from the first polynomial)
3. \(-2p - 3p\) (combining terms from both polynomials)
4. \(3 + 4\) (combining constant terms)

Putting it all together, we get:
\[
p^4 - 5p^2 - 5p + 7
\]

So, the sum of the polynomials \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\) is:
\[
\boxed{p^4 - 5p^2 - 5p + 7}
\]