1. Which polynomial does the model represent? (One big black square, two white rectangles, one black rectangle, one white cube, and three black cubes.)
This is all I need.
@Mrs. Sue @Reed
To determine which polynomial the model represents, we need to analyze the shapes in the model and their corresponding quantities.
From the description you've provided, we have:
- One big black square
- Two white rectangles
- One black rectangle
- One white cube
- Three black cubes
Let's assign variables to each shape:
- Let's say the big black square represents x.
- Let's say each white rectangle represents y.
- Let's say the black rectangle represents z.
- Let's say the white cube represents w.
- Let's say each black cube represents a.
Now, let's represent the given quantities in terms of these variables:
- One big black square (x^2)
- Two white rectangles (2y)
- One black rectangle (z)
- One white cube (w^3)
- Three black cubes (3a^3)
Putting it all together, the polynomial that represents the model is:
x^2 + 2y + z + w^3 + 3a^3
To identify the polynomial represented by the model, we need to understand the relationship between the different shapes and their corresponding variables. Let's analyze the given information:
- One big black square: This represents a term that involves a variable raised to the power of 2 (x^2).
- Two white rectangles: These represent two terms that involve a variable raised to the power of 1 (x).
- One black rectangle: This represents a term that involves a variable raised to the power of 1 (x).
- One white cube: This represents a term that involves a variable raised to the power of 3 (x^3).
- Three black cubes: These represent three terms that involve a variable raised to the power of 3 (x^3).
Now that we have identified the different terms based on their shapes, let's put them together to form the polynomial.
The polynomial can be written as:
x^3 + 3x^3 + x + 2x + x^2
To simplify this expression, we combine like terms:
4x^3 + 3x^2 + 3x
Therefore, the polynomial represented by the model is 4x^3 + 3x^2 + 3x.