Question

add the polynomial expressions 3 - 2p - 5p^2 and p^4 - 3p + 4

Answer 1

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

1. Write down the polynomials:

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

2. Next, rewrite them in standard form (descending powers of \(p\)):

\[
0p^4 + 0p^3 - 5p^2 - 2p + 3
\]
\[
1p^4 + 0p^3 + 0p^2 - 3p + 4
\]

3. Now, add them together by adding the coefficients of like terms:

- For \(p^4\): \(0 + 1 = 1\)
- For \(p^3\): \(0 + 0 = 0\)
- For \(p^2\): \(-5 + 0 = -5\)
- For \(p\): \(-2 - 3 = -5\)
- Constant: \(3 + 4 = 7\)

4. Combine these results:

\[
1p^4 + 0p^3 - 5p^2 - 5p + 7
\]

5. Finally, write the polynomial in standard form:

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

So, the sum of the polynomials \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\) is:

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