1. which polynomial does the model represent
(Model shows: 1 big black square, 2 long white rectangles, 3 long black rectangles, 3 small white squares, 1 small black square)
a) -x^3+2x^2-3x+2
b) x^2+x-2******
c) -x^2-x+2
d) -x^2+x-2
If black is + and white is - then you are correct.
Based on the given model, we can count the number of each shape to determine the polynomial.
- There is 1 big black square, which represents a term with an exponent of 2 (x^2).
- There are 2 long white rectangles, which represents a term with a coefficient of 2 (2x).
- There are 3 long black rectangles, which also represents a term with a coefficient of -3 (-3x).
- There are 3 small white squares, which represents a term with a coefficient of 2 (2).
Putting these terms together, the polynomial that the model represents is:
b) x^2+x-2
To determine which polynomial the model represents, we need to analyze the different parts of the model.
Let's start by examining the big black square. The big black square represents the coefficient of the highest degree term in the polynomial.
Looking at the model, we have 1 big black square, which suggests that the highest degree term would be a power of x raised to 1, which is x.
Next, let's consider the long white rectangles. These rectangles represent the coefficients of the next highest degree term in the polynomial. In this case, we have 2 long white rectangles.
Following that, we have the long black rectangles, which represent the coefficients of the next degree term. In the model, we have 3 long black rectangles.
Moving on, we have the small white squares, which correspond to the coefficients of the next lower degree term. The model shows 3 small white squares.
Finally, we have the small black square, which indicates the constant term in the polynomial. In this case, we have 1 small black square.
Based on this analysis, we can write the polynomial expression as follows:
x^3 + 2x^2 + 3x + 3
Now let's compare this expression to the options provided:
a) -x^3 + 2x^2 - 3x + 2: This option does not match the polynomial we derived.
b) x^2 + x - 2: This option does not match the polynomial we derived.
c) -x^2 - x + 2: This option does not match the polynomial we derived.
d) -x^2 + x - 2: This option does not match the polynomial we derived.
Based on the comparison, none of the provided options match the polynomial expression we derived from the model. It is possible that the correct polynomial expression is not listed among the provided options, or there may be an error in the options provided.