Question

Add the polynomial expressions 3−2p−5p2 and p4−3p+4 .(1 point)%0D%0AResponses%0D%0A%0D%0Ap4−5p2−5p+7%0D%0Ap superscript 4 baseline minus 5 p squared minus 5 p plus 7%0D%0A%0D%0A−4p2−5p+7%0D%0Anegative 4 p squared minus 5 p plus 7%0D%0A%0D%0Ap4−5p2−6p+7%0D%0Ap superscript 4 baseline minus 5 p squared minus 6 p plus 7%0D%0A%0D%0A−5p2−4p+7

Answer 1

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

1. Write the expressions together: \[ (3 - 2p - 5p^2) + (p^4 - 3p + 4) \]

2. Rearranging and grouping by powers of \( p \): \[ p^4 - 5p^2 + (-2p - 3p) + (3 + 4) \]

3. Combine the like terms:

   • The \( p^4 \) term remains \( p^4 \).
   • Combine the \( -5p^2 \) term: still \( -5p^2 \).
   • Combine the \( -2p \) and \( -3p \) terms: \( -2p - 3p = -5p \).
   • Combine the constants: \( 3 + 4 = 7 \).

Now, putting it all together: \[ p^4 - 5p^2 - 5p + 7 \]

So the answer is: \[ \boxed{p^4 - 5p^2 - 5p + 7} \]