Question

Find the sum. (4n3−2n2−5n)+(2n4+6n2+2n +8) (1 point) Responses 6n7+4n2−3n+8 6 n to the 7th power plus 4 n squared minus 3 n plus 8 2n7+8n4+7n+8 2 n to the 7th power plus 8 n to the 4th power plus 7 n plus 8 2n4+4n3+4n2−3n+8 2 n to the 4th power plus 4 n cubed plus 4 n squared minus 3 n plus 8 2n4+4n3+8n2+7n+8

Answer 1

To find the sum of the two polynomials \((4n^3 - 2n^2 - 5n) + (2n^4 + 6n^2 + 2n + 8)\), we first align the like terms:

1. **First Polynomial**:
\(4n^3 - 2n^2 - 5n\)

2. **Second Polynomial**:
\(2n^4 + 6n^2 + 2n + 8\)

Now, we can rewrite the expression by combining them:

\[
(4n^3 + 2n^4 - 2n^2 + 6n^2 - 5n + 2n + 8)
\]

Next, we combine the coefficients of like terms:

- **For \(n^4\)**:
\(2n^4\)

- **For \(n^3\)**:
\(4n^3\)

- **For \(n^2\)**:
\(-2n^2 + 6n^2 = 4n^2\)

- **For \(n\)**:
\(-5n + 2n = -3n\)

- **Constant term**:
\(8\)

Now we can write the sum:

\[
2n^4 + 4n^3 + 4n^2 - 3n + 8
\]

Therefore, the sum of the polynomials is:

\(\boxed{2n^4 + 4n^3 + 4n^2 - 3n + 8}\)