To multiply the given polynomials \( (2x - 7)(3x^2 + 7x - 8) \), we can use the distributive property (also known as the FOIL method for binomials):
1. **Multiply \( 2x \) by each term in the second polynomial**:
\[
2x \cdot 3x^2 = 6x^3
\]
\[
2x \cdot 7x = 14x^2
\]
\[
2x \cdot (-8) = -16x
\]
2. **Multiply \( -7 \) by each term in the second polynomial**:
\[
-7 \cdot 3x^2 = -21x^2
\]
\[
-7 \cdot 7x = -49x
\]
\[
-7 \cdot (-8) = 56
\]
3. **Now, combine all the results**:
\[
6x^3 + (14x^2 - 21x^2) + (-16x - 49x) + 56
\]
4. **Combine like terms**:
\[
6x^3 + (-7x^2) + (-65x) + 56
\]
So, the resulting polynomial in descending order is:
\[
6x^3 - 7x^2 - 65x + 56
\]
Now we can identify the coefficients for each term:
- The coefficient of \( x^3 \) is **6**.
- The coefficient of \( x^2 \) is **-7**.
- The coefficient of \( x \) is **-65**.
- The coefficient of the constant is **56**.
### Final Answers
- The value of the coefficient of the \( x^3 \) is **6**.
- The value of the coefficient of the \( x^2 \) is **-7**.
- The value of the coefficient of the \( x \) is **-65**.
- The value of the coefficient of the constant is **56**.