Question

Which polynomial represents the sum below?
(14x2-14) +(-10x2 - 10x + 10)
04x2-10x+24
04x2-10x-4
024x2-24x-10
014x3+4x2+10x-4

Answer 1

To find the polynomial that represents the sum \((14x^2 - 14) + (-10x^2 - 10x + 10)\), we will first combine like terms.

1. Start with the expression:
\[
(14x^2 - 14) + (-10x^2 - 10x + 10)
\]

2. Remove the parentheses:
\[
14x^2 - 14 - 10x^2 - 10x + 10
\]

3. Now, combine like terms:
- Combine \(14x^2\) and \(-10x^2\):
\[
14x^2 - 10x^2 = 4x^2
\]
- For the \(x\) terms, there is only \(-10x\):
\[
-10x
\]
- Finally, combine the constant terms \(-14\) and \(+10\):
\[
-14 + 10 = -4
\]

4. Therefore, the resulting polynomial is:
\[
4x^2 - 10x - 4
\]

This matches the second option from your provided choices, which is:
\[
04x^2 - 10x - 4
\]

Thus, the answer is:
\[
\boxed{04x^2 - 10x - 4}
\]