Multiply the following polynomials and write the resulting polynomials in descending order.

To multiply the polynomials \((2x - 7)(3x^2 + 7x - 8)\), we'll use the distributive property.

1. Distributing \(2x\) to each term in \(3x^2 + 7x - 8\):
\[
2x \cdot 3x^2 = 6x^3
\]
\[
2x \cdot 7x = 14x^2
\]
\[
2x \cdot (-8) = -16x
\]

2. Distributing \(-7\) to each term in \(3x^2 + 7x - 8\):
\[
-7 \cdot 3x^2 = -21x^2
\]
\[
-7 \cdot 7x = -49x
\]
\[
-7 \cdot (-8) = 56
\]

Now, combine all these results:
- From \(2x\) we got: \(6x^3 + 14x^2 - 16x\)
- From \(-7\) we got: \(-21x^2 - 49x + 56\)

Combine the like terms:
- \(6x^3\) (only one term)
- \(14x^2 - 21x^2 = -7x^2\)
- \(-16x - 49x = -65x\)
- \(56\) (only one term)

Putting it all together, the result of the multiplication is:
\[
6x^3 - 7x^2 - 65x + 56
\]

Now, we can identify the coefficients for each power of \(x\):
- Coefficient of \(x^3\) is **6**
- Coefficient of \(x^2\) is **-7**
- Coefficient of \(x\) is **-65**
- Constant term (coefficient of \(x^0\)) is **56**

Putting the answers neatly:
- The value of the coefficient of \(x^3\) is **6**
- The value of the coefficient of \(x^2\) is **-7**
- The value of the coefficient of \(x\) is **-65**
- The value of the coefficient of the constant is **56**