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

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Responses

Answer 1

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

Let's rewrite both polynomials:

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

Now, let's add them together:

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

Now, combine 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:

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

Thus, the sum of the two polynomials is:

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