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 \( p^4 - 3p + 4 \), you need to combine like terms:

1. Write the two polynomials one under the other, aligning like terms:

\[ \begin{array}{r} 3 \ -2p \ -5p^2 \ \hline \end{array} + \begin{array}{r} p^4 \ -3p \ 4 \ \hline \end{array} \]

2. Now, combine all the like terms:

• The highest degree term is \( p^4 \).
• The \( p^2 \) term is \( -5p^2 \).
• The \( p \) terms are \( -2p - 3p = -5p \).
• The constant terms are \( 3 + 4 = 7 \).

Putting it all together, we get:

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

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

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