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
To determine the polynomial that the model represents, we need to analyze the pattern of the shapes and relate it to the terms in the polynomial options. Let's go through each term:
1 big black square: This represents a coefficient of x^2.
2 long blank rectangles: This represents a coefficient of 2x.
3 long rectangles: This represents a coefficient of -3x.
3 small blank squares: This represents a coefficient of 3.
1 small blank square: This represents a constant term of 2.
Putting all these terms together, the polynomial that the model represents is:
- x^2 + 2x - 3x + 3 + 2
Now let's simplify this expression:
- x^2 + (2x - 3x) + (3 + 2)
Combining like terms:
- x^2 - x + 5
Comparing this simplified expression to the given options, we find that the polynomial that the model represents is:
c.) -x^2 - x + 2
To determine which polynomial the model represents, we need to analyze the coefficients and degrees of the terms in each answer choice.
Let's break down the given model:
1 big black square: This represents a term with a coefficient of 1 and a degree of 2 since it's square-shaped.
2 long blank rectangles: Each of these represents a term with a coefficient of 2 and a degree of 1 since they're rectangular-shaped.
3 long rectangles: Each of these represents a term with a coefficient of 3 and a degree of 1.
3 small blank squares: Each of these represents a term with a coefficient of -3 and a degree of 2.
1 small blank square: This represents a term with a coefficient of 1 and a degree of 2.
Now, let's compare the model to the answer choices:
a) -x^3 + 2x^2 - 3x + 2: This choice has a term with a coefficient of -3 and degree of 2, but it has additional terms with higher degrees (cubic x^3 and linear -3x terms) that are not present in the model. So, option a is not correct.
b) x^2 + x - 2: This choice has a term with a coefficient of 1 and degree of 2, and two terms with coefficients and degrees matching the model. So, option b is a potential fit.
c) -x^2 - x + 2: This choice has terms with matching degrees (2 and 1), but the coefficients do not match the model. So, option c is not correct.
d) -x^2 + x - 2: This choice has a term with a coefficient of -1 and degree of 2, and two terms with coefficients and degrees matching the model. Note that the sign of the coefficient in option d is positive for the term with degree 1, while it is negative in the model. Therefore, option d is not correct.
Based on the analysis, the polynomial that matches the given model is option b) x^2 + x - 2.