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

Question

A -5p^2 - 4p + 7
B p^4 - 5p^3 - 5p + 7
C -4p^2 - 5p + 7
D p^4 - 5p^2 - 6p + 7

Answer 1

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

1. Write down both polynomials:

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

2. Combine them into one expression:

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

3. Rearrange and group like terms:

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

4. Combine the coefficients:

   • For \(p^4\): just \(p^4\)
   • For \(p^2\): \(-5p^2\)
   • For \(p\): \(-2p - 3p = -5p\)
   • Constant: \(3 + 4 = 7\)

5. Putting it all together, we get:

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

So the answer is:

D: \(p^4 - 5p^2 - 5p + 7\)