Question

Find the difference between
(6x^2 - x + 10) - (3x+8)

A. 6x^2 + 2x + 18
B. 6x^2 - 4x - 18
C. 6x^2 + 2x + 2
D. 6x^2 - 4x + 2

Answer 1

To find the difference between the two polynomial expressions \((6x^2 - x + 10)\) and \((3x + 8)\), we can rewrite the expression as:

\[
(6x^2 - x + 10) - (3x + 8)
\]

This involves distributing the negative sign to both terms in the second polynomial:

\[
6x^2 - x + 10 - 3x - 8
\]

Now we can combine like terms. First, we group the \(x^2\) term, the \(x\) terms, and the constant terms:

1. **\(x^2\) term:**
- There is only one term: \(6x^2\).

2. **\(x\) terms:**
- Combine \(-x\) and \(-3x\):
\[
-x - 3x = -4x
\]

3. **Constant terms:**
- Combine \(10\) and \(-8\):
\[
10 - 8 = 2
\]

Now we can write the final polynomial form:

\[
6x^2 - 4x + 2
\]

So, the difference is:

\[
\boxed{D. \, 6x^2 - 4x + 2}
\]