Question

Multiply the following polynomials and write the resulting polynomial in descending order.
(3x - 8) (2x^2 + 4x - 9)
The value of the coefficient of the x^3 term is ___.
The value of the coefficient of the x^2 term is ___.
The value of the coefficient of the x term is ___.
The value of the constant is ___.

Answer 1

To multiply the polynomials \( (3x - 8)(2x^2 + 4x - 9) \), we'll use the distributive property (FOIL method) to find the product.

1. **Multiply \(3x\) by each term in the second polynomial:**
- \(3x \cdot 2x^2 = 6x^3\)
- \(3x \cdot 4x = 12x^2\)
- \(3x \cdot (-9) = -27x\)

2. **Multiply \(-8\) by each term in the second polynomial:**
- \(-8 \cdot 2x^2 = -16x^2\)
- \(-8 \cdot 4x = -32x\)
- \(-8 \cdot (-9) = 72\)

3. **Combine all the terms together:**
\[
6x^3 + 12x^2 - 27x - 16x^2 - 32x + 72
\]

4. **Combine like terms:**
- For \(x^2\): \(12x^2 - 16x^2 = -4x^2\)
- For \(x\): \(-27x - 32x = -59x\)

5. **Write the resulting polynomial in descending order:**
\[
6x^3 - 4x^2 - 59x + 72
\]

Now, we can identify the coefficients:

- The coefficient of the \(x^3\) term is **6**.
- The coefficient of the \(x^2\) term is **-4**.
- The coefficient of the \(x\) term is **-59**.
- The constant term is **72**.

**Final answers:**
- The value of the coefficient of the \(x^3\) term is **6**.
- The value of the coefficient of the \(x^2\) term is **-4**.
- The value of the coefficient of the \(x\) term is **-59**.
- The value of the constant is **72**.