Add the polynomial expressions 3−2p−5p2 and p4−3p+4 .(1 point)

Question

Responses

p4−5p2−5p+7
p superscript 4 baseline minus 5 p squared minus 5 p plus 7

−5p2−4p+7
negative 5 p squared minus 4 p plus 7

p4−5p2−6p+7
p superscript 4 baseline minus 5 p squared minus 6 p plus 7

−4p2−5p+7

Answer 1

To add the polynomial expressions \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), we start by writing them together:

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

Next, we combine like terms:

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

Now we can write the combined polynomial:

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

So, the final expression is:

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

The correct response is: p⁴ - 5p² - 5p + 7.