which polynomial does the model represent (Model shows: 1 big black square, 2 long blank rectangles, 3 long rectangles, 3 small blank squares, 1 small blank square)

a.) -x^3+2x^2-3x+2
b.)x^2+x-2
c.)-x^2-x+2
d.)-x^2+x-2

The description seems a bit unclear; however, we will try to associate each shape with a term of a polynomial.

1 big black square = -x^2
2 long blank rectangles = +2x
3 long rectangles = -3x
3 small blank squares = some discrepancy, as there's no 3 or -3 constant term in any option, could be a typo in the model.
1 small blank square = +1

Combining these, we get -x^2 +2x -3x +1 or -x^2 -x +1, but none of the options match exactly. The closest one is option c.) -x^2 -x +2 which might represent the model with a typo or misinterpretation.

To determine which polynomial the model represents, we need to analyze the number of each shape shown and compare it to the coefficients of the polynomial options given.

Let's break down the model:

1 big black square, which represents a term of degree 4.
2 long blank rectangles, which represent a term of degree 3.
3 long rectangles, which represent a term of degree 2.
3 small blank squares, which represent a term of degree 1.
1 small blank square, which represents a term of degree 0 (constant term).

Now, let's compare these numbers to the coefficients in each polynomial option:

a.) -x^3 + 2x^2 - 3x + 2 : This polynomial does not match the model since it has a term of degree 3 but not the other degrees present in the model.

b.) x^2 + x - 2 : This polynomial does not match the model since it is missing terms of degree 3 and 0.

c.) -x^2 - x + 2 : This polynomial matches the model since it has the same degrees present, although the signs may differ.

d.) -x^2 + x - 2 : This polynomial does not match the model since it is missing terms of degrees 3 and 1.

Therefore, the correct polynomial that the model represents is option c.) -x^2 - x + 2.

To determine which polynomial the model represents, we need to analyze the number of each type of shape in the model.

From the model description, we have:
- 1 big black square
- 2 long blank rectangles
- 3 long rectangles
- 3 small blank squares
- 1 small blank square

Now, let's compare this to the given polynomial options:

a.) -x^3+2x^2-3x+2
b.) x^2+x-2
c.) -x^2-x+2
d.) -x^2+x-2

First, let's check option a:
- It includes a cubic term (-x^3), which means it should involve a large number of shapes, but the model only has 1 big black square.

Now, let's check option b:
- The model has 2 long blank rectangles, which matches the quadratic term (x^2) in this option.
- The model does not have an x term, but option b includes an x term (x).
- The model does not have a constant term, but option b includes a constant term (-2).

Next, let's check option c:
- The model has 2 long blank rectangles, which matches the quadratic term (-x^2) in this option.
- The model has 3 small blank squares, which matches the linear term (-x) in this option.
- The model does not have a constant term, but option c includes a constant term (2).

Lastly, let's check option d:
- The model has 2 long blank rectangles, which matches the quadratic term (-x^2) in this option.
- The model does not have an x term, but option d includes an x term (x).
- The model does not have a constant term, but option d includes a constant term (-2).

Comparing all the options, we can see that the model matches option c, which is -x^2-x+2.

Therefore, the polynomial that the model represents is c.) -x^2-x+2.