Question

Which polynomial represents the difference below?
(8x^2 + 9) -(3x^2 + 2x + 5)

Answer 1

To find the polynomial representing the difference \( (8x^2 + 9) - (3x^2 + 2x + 5) \), we will first distribute the negative sign to the terms inside the second parentheses and then combine like terms.

1. Rewrite the expression:
\[
8x^2 + 9 - (3x^2 + 2x + 5)
\]

2. Distributing the negative sign:
\[
8x^2 + 9 - 3x^2 - 2x - 5
\]

3. Combine like terms:
- Combine \( 8x^2 \) and \( -3x^2 \):
\[
8x^2 - 3x^2 = 5x^2
\]

- Combine the constant terms \( 9 \) and \( -5 \):
\[
9 - 5 = 4
\]

- There is no \( x \) term in the first polynomial, so the \( -2x \) stands alone.

4. Putting it all together:
\[
5x^2 - 2x + 4
\]

Thus, the polynomial that represents the difference is:
\[
\boxed{5x^2 - 2x + 4}
\]