Question

Which polynomial represents the difference below?
5x^2+9x+3
- (6x^2 - 3x)

Answer 1

To find the difference between the polynomials \(5x^2 + 9x + 3\) and \(6x^2 - 3x\), we perform the subtraction as follows:

\[
5x^2 + 9x + 3 - (6x^2 - 3x)
\]

Distributing the negative sign across the second polynomial:

\[
5x^2 + 9x + 3 - 6x^2 + 3x
\]

Now, we can combine like terms:

1. Combine the \(x^2\) terms:
\[
5x^2 - 6x^2 = -1x^2
\]

2. Combine the \(x\) terms:
\[
9x + 3x = 12x
\]

3. The constant term remains unchanged:
\[
3
\]

Now, putting it all together, we get:

\[
-1x^2 + 12x + 3
\]

This can also be written as:

\[
- x^2 + 12x + 3
\]

Thus, the polynomial that represents the difference is:

\[
-x^2 + 12x + 3
\]