To find the difference between the polynomials [tex]\(7x^2 + 8\)[/tex] and [tex]\(4x^2 + x + 6\)[/tex], let's subtract the coefficients from each other step-by-step.
1. Identify the corresponding terms:
- The [tex]\(x^2\)[/tex] terms are [tex]\(7x^2\)[/tex] and [tex]\(4x^2\)[/tex].
- The [tex]\(x\)[/tex] term is [tex]\(0x\)[/tex] (for [tex]\(7x^2 + 8\)[/tex]) and [tex]\(x\)[/tex] (for [tex]\(4x^2 + x + 6\)[/tex]).
- The constant terms are [tex]\(8\)[/tex] and [tex]\(6\)[/tex].
2. Subtract the [tex]\(x^2\)[/tex] terms:
[tex]\[
7x^2 - 4x^2 = (7 - 4)x^2 = 3x^2
\][/tex]
3. Subtract the [tex]\(x\)[/tex] terms:
[tex]\[
0x - 1x = -1x = -x
\][/tex]
4. Subtract the constant terms:
[tex]\[
8 - 6 = 2
\][/tex]
Putting it all together, the difference between the two polynomials is:
[tex]\[
3x^2 - x + 2
\][/tex]
Therefore, the polynomial that represents the difference is:
C. [tex]\(3x^2 - x + 2\)[/tex]
