To find the polynomial that represents the difference between [tex]\(2x^2 + 7x + 6\)[/tex] and [tex]\(3x^2 - x\)[/tex], we can follow these steps:
1. Write the given polynomials:
[tex]\[
2x^2 + 7x + 6
\][/tex]
[tex]\[
3x^2 - x
\][/tex]
2. Subtract the second polynomial from the first polynomial term-by-term:
- For the [tex]\(x^2\)[/tex] term: [tex]\(2x^2 - 3x^2\)[/tex]
- For the [tex]\(x\)[/tex] term: [tex]\(7x - (-x) = 7x + x\)[/tex]
- For the constant term: [tex]\(6 - 0\)[/tex]
3. Perform the subtraction for each term:
- For the [tex]\(x^2\)[/tex] term: [tex]\(2x^2 - 3x^2 = -x^2\)[/tex]
- For the [tex]\(x\)[/tex] term: [tex]\(7x + x = 8x\)[/tex]
- For the constant term: [tex]\(6 - 0 = 6\)[/tex]
4. Combine the resulting terms to form the final polynomial:
[tex]\[
-x^2 + 8x + 6
\][/tex]
Thus, the polynomial that represents the difference is [tex]\(-x^2 + 8x + 6\)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{-x^2 + 8x + 6}
\][/tex]
Which corresponds to option:
[tex]\[
\boxed{C}
\][/tex]
