Question

Add the polynomial expressions 3 − 2p − 5p^2 and p4 − 3p + 4.
A) p^4 - 5p^2 - 5p + 7
B) -4p^2 - 5p + 7
C) p^4 - 5p^2 - 6p + 7
D) -5p^2 - 4p + 7

Answer 1

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

1. Start with the first polynomial:
\[
3 - 2p - 5p^2
\]

2. Then, write the second polynomial beneath it:
\[
p^4 - 3p + 4
\]

3. Now, let's line them up by their degrees:
\[
\begin{align*}
&\phantom{+} p^4 \\
&- 5p^2 \\
&- 2p \\
&+ 3 \\
&+ 4 \\
&- 3p
\end{align*}
\]

4. Combine the like terms:
- The \(p^4\) term: \(p^4\)
- The \(p^2\) term: \(-5p^2\)
- The \(p\) terms: \(-2p - 3p = -5p\)
- The constant terms: \(3 + 4 = 7\)

Thus, adding them together gives:
\[
p^4 - 5p^2 - 5p + 7
\]

The correct answer is:
\[
\text{A) } p^4 - 5p^2 - 5p + 7
\]