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:

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