Question

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

(2x−7)(3x2+7x−8)
(4 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
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 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**.