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

Question

(2x−7)(3x2+7x−8)
(4 points)
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The value of the coefficient of the x3
is Response area

The value of the coefficient of the x2
is Response area
The value of the coefficient of the x
is Response area
The value of the coefficient of the constant is

Answer 1

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.