Question

Add the polynomial expression 3 - 2p - 5p squared and p to the fourth minus 3p + 4

Answer 1

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

1. Write down the first polynomial:
\[
3 - 2p - 5p^2
\]
2. Write down the second polynomial:
\[
p^4 - 3p + 4
\]

Now, we can align like terms from both polynomials:

\[
\begin{align*}
& 0p^4 + 0p^3 - 5p^2 - 2p + 3 \\
& + 1p^4 + 0p^3 + 0p^2 - 3p + 4 \\
\end{align*}
\]

Now, we can combine the like terms:
- For \(p^4\): \(0 + 1 = 1p^4\)
- For \(p^3\): \(0 + 0 = 0p^3\)
- For \(p^2\): \(-5 + 0 = -5p^2\)
- For \(p\): \(-2 - 3 = -5p\)
- For the constant terms: \(3 + 4 = 7\)

Putting these together, we get the final result:

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

Thus, the sum of the two polynomial expressions is:
\[
\boxed{p^4 - 5p^2 - 5p + 7}
\]