which polynomial does the model represent (Model shows: 1 big black square, 1 long black rectangles, 2 long blank rectangles, 3 small black 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
A) -x^3+2x^2-3x+2
To determine which polynomial the model represents, let's analyze the model step-by-step:
1. There is 1 big black square, which represents x^3.
2. There is 1 long black rectangle, which represents 2x^2.
3. There are 2 long blank rectangles, which represent -2x^2.
4. There are 3 small black squares, which represent 3x.
5. There is 1 small blank square, which represents -1x or simply -x.
Putting all the components together, the polynomial that the model represents is:
1x^3 + 2x^2 - 2x^2 + 3x - x
Simplifying the expression, we get:
x^3 + x
Comparing this expression to the given options, we find that the correct polynomial representation for the model is:
b.) x^2 + x - 2
To determine which polynomial the model represents, we need to interpret the model and match it with the polynomial expression.
Let's break down the model representation:
- 1 big black square represents the term x^3.
- 1 long black rectangle represents the term 2x^2.
- 2 long blank rectangles represent the term -2x^2 since they show a subtraction by subtracting two long rectangles.
- 3 small black squares represent the term -3x.
- 1 small blank square represents the constant term, which is +2.
Now, let's form the polynomial expression:
Starting with the highest power of x, which is x^3, we have:
x^3 - 2x^2 - 3x + 2
Comparing this expression with the given choices, we find that it matches with option A:
A) -x^3 + 2x^2 - 3x + 2.
Therefore, the polynomial that the model represents is -x^3 + 2x^2 - 3x + 2.