Question

ric multiplied (6x2−7x+4.7)(x2−2.8)
using an area model.

Complete the blank spaces in the area model and determine the product in standard form.

(5 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.
6x2
−7x
4.7
x2
−7x3
Response area
−2.8
−13.16
The product in standard form is

Answer 1

To multiply the two polynomials \( (6x^2 - 7x + 4.7)(x^2 - 2.8) \) using an area model, we first set up a grid where we break the polynomials into their individual terms and multiply each term accordingly.

1. Set up the area model:
- On the top, put the terms of the first polynomial: \( 6x^2 \), \( -7x \), and \( 4.7 \).
- On the side, put the terms of the second polynomial: \( x^2 \) and \( -2.8 \).

2. Now fill in the area grid by multiplying each pair of terms:

- Top left: \( 6x^2 \cdot x^2 = 6x^4 \)
- Top middle: \( 6x^2 \cdot (-2.8) = -16.8x^2 \)
- Middle left: \( -7x \cdot x^2 = -7x^3 \)
- Middle middle: \( -7x \cdot (-2.8) = 19.6x \)
- Bottom left: \( 4.7 \cdot x^2 = 4.7x^2 \)
- Bottom middle: \( 4.7 \cdot (-2.8) = -13.16 \)

Now, let’s fill in the area model:
- \( 6x^4 \) in the top left.
- \( -16.8x^2 \) in the top middle.
- \( -7x^3 \) in the middle left.
- \( 19.6x \) in the middle middle.
- \( 4.7x^2 \) in the bottom left.
- \( -13.16 \) in the bottom middle.

3. Now combine all terms based on their degrees:
- The \( x^4 \) term: \( 6x^4 \)
- The \( x^3 \) term: \( -7x^3 \)
- The \( x^2 \) terms: \( -16.8x^2 + 4.7x^2 = -12.1x^2 \)
- The \( x \) term: \( 19.6x \)
- The constant term: \( -13.16 \)

Combining these, the product of the two polynomials in standard form is:
\[
6x^4 - 7x^3 - 12.1x^2 + 19.6x - 13.16
\]

So the final response for the product in standard form is:
\[
6x^4 - 7x^3 - 12.1x^2 + 19.6x - 13.16
\]