Add the polynomial expression 3-2p-5p² and p⁴-3p+4.

Answer 1

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

First, write the two polynomials together:

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

Now, group the like terms:

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

Now we can combine them:

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

Thus, the sum of the two polynomial expressions is:

\[ \boxed{p^4 - 5p^2 - 5p + 7} \]