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

Question

(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.