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

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

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

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

Answer 1

To add the polynomial expressions \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), we align the terms by their degrees:

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

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

Now, we can add them together, combining like terms:

\[ (p^4) + (0p^3) + (-5p^2) + (-2p - 3p) + (3 + 4) \]

Adding these terms gives:

\[ p^4 + 0p^3 - 5p^2 - 5p + 7 \]

So, the final combined polynomial is:

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

From the options given, the correct response is:

p^4 - 5p^2 - 5p + 7