Add the polynomial

Question

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

Answer 1

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

Here are the expressions lined up for addition:

\[ \begin{align*} & \quad 3 \quad - 2p \quad - 5p^2 \

• & \quad 4 \quad - 3p \quad + p^4 \ \end{align*} \]

Now we add the corresponding terms:

• Constant terms: \(3 + 4 = 7\)
• Linear terms: \(-2p - 3p = -5p\)
• Quadratic term: \(-5p^2\) (there's no quadratic term in the second polynomial)
• Cubic term: There are no cubic terms in either polynomial.
• Quartic term: \(p^4\) (there's no quartic term in the first polynomial)

Now, writing it all together, we have:

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

Thus, the sum of the polynomial expressions is:

\[ \boxed{p^4 - 5p^2 - 5p + 7} \]