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

(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

1 answer

To multiply the polynomials \((2x−7)(3x^2+7x−8)\), we will 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, let's combine all the results: \[ 6x^3 + 14x^2 - 16x - 21x^2 - 49x + 56 \]

Next, combine like terms:

  • For \(x^2\): \(14x^2 - 21x^2 = -7x^2\)
  • For \(x\): \(-16x - 49x = -65x\)

The resulting polynomial is: \[ 6x^3 - 7x^2 - 65x + 56 \]

Now, we can identify the coefficients:

  • 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 term is \(56\).

So, the values for the response areas are:

  • 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.