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

Question

p4−5p2−6p+7

−5p2−4p+7

p4−5p2−5p+7

−4p2−5p+7

Answer 1

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

1. Start by writing both polynomials:

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

2. Now, arrange them and add them together:

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

3. Combine the constant terms:

   \[ 3 + 4 = 7 \]

4. Combine the \(p\) terms:

   \[ -2p - 3p = -5p \]

5. The \(p^2\) term remains:

   \[ -5p^2 \]

6. The \(p^4\) term remains:

   \[ p^4 \]

7. Now, put it all together by arranging the terms in descending order of power:

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

So, the final expression after adding the two polynomials is:

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

The correct answer from the options you provided is:

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