Question

What is the sum of the polynomials 3^2+2x+1 and 2x^3-x+4?
A) 5^2+x+5
B) 5x^+x+3
C) 5x^2+x+4
D) 5x^2+x+6

Answer 1

pick one

Answer 2

To find the sum of the polynomials \(3^2 + 2x + 1\) and \(2x^3 - x + 4\), we first simplify the first polynomial.

Calculate \(3^2\):
\[
3^2 = 9
\]
Thus, the first polynomial can be rewritten as:
\[
9 + 2x + 1
\]
which simplifies to:
\[
10 + 2x
\]

Now we add this to the second polynomial \(2x^3 - x + 4\):
\[
(10 + 2x) + (2x^3 - x + 4)
\]

Next, we combine like terms:
- The \(x^3\) term: \(2x^3\)
- The \(x\) terms: \(2x - x = x\)
- The constant terms: \(10 + 4 = 14\)

Combining all the terms gives us:
\[
2x^3 + x + 14
\]

Now we need to compare this with the answer choices provided:
A) \(5^2 + x + 5\)
B) \(5x^2 + x + 3\)
C) \(5x^2 + x + 4\)
D) \(5x^2 + x + 6\)

None of the answer choices match \(2x^3 + x + 14\). Therefore, either there was a misunderstanding in the expected sum or the options listed do not correctly correspond to the calculated polynomial sum.

In conclusion, the directly calculated sum of the polynomials is:
\[
2x^3 + x + 14
\]

None of the options provided match this result.

Answer 3

Since none of the options match the correct sum \(2x^3 + x + 14\), I will choose the option that appears to be the closest structure-wise, which is Option A) \(5^2 + x + 5\).

This choice is purely arbitrary, as the correct polynomial does not match any provided options. Shall I help you with anything else?