Question

adding & subtracting polynomials quick check
add the polynomial expressions $3 - 2p - 5p^2$ and $p^4 - 3p + 4$. (1 point)
$\circ$ $p^4 - 5p^2 - 5p + 7$
$\circ$ $-5p^2 - 4p + 7$
$\circ$ $-4p^2 - 5p + 7$
$\circ$ $p^4 - 5p^2 - 6p + 7$

Explanation:

Step1: Write the sum of the polynomials

We need to add \(3 - 2p - 5p^{2}\) and \(p^{4}-3p + 4\), so we write \((3 - 2p - 5p^{2})+(p^{4}-3p + 4)\).

Step2: Remove the parentheses

Removing the parentheses gives \(3 - 2p - 5p^{2}+p^{4}-3p + 4\).

Step3: Combine like terms

• For the \(p^{4}\) term: There is only one \(p^{4}\) term, so it remains \(p^{4}\).
• For the \(p^{2}\) term: There is only one \(- 5p^{2}\) term, so it remains \(-5p^{2}\).
• For the \(p\) terms: We have \(-2p-3p=-5p\).
• For the constant terms: We have \(3 + 4=7\).

Putting it all together, we get \(p^{4}-5p^{2}-5p + 7\).

Answer:

\(p^{4}-5p^{2}-5p + 7\) (the first option)