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# Explanation:
## Step1: Let the unknown polynomial be $ A $. So the equation is $ -9x^3 - 5x^2 + x + 1 = A - (-4x^3 + x^2 + 6x) $.
## Step2: To find $ A $, we can rewrite the equation as $ A = -9x^3 - 5x^2 + x + 1 + (-4x^3 + x^2 + 6x) $.
## Step3: Combine like terms. For the $ x^3 $ terms: $ -9x^3 + (-4x^3) = -13x^3 $. For the $ x^2 $ terms: $ -5x^2 + x^2 = -4x^2 $. For the $ x $ terms: $ x + 6x = 7x $. The constant term is $ 1 $. So $ A = -13x^3 - 4x^2 + 7x + 1 $.
# Answer:
The unknown polynomial (the top box) is $ -13x^3 - 4x^2 + 7x + 1 $, the left bottom box is $ -13x^3 - 4x^2 + 7x + 1 $ (the whole), and the right bottom box is $ -4x^3 + x^2 + 6x $ (the part being subtracted). So filling in the model:

Top box: $ \boldsymbol{-13x^3 - 4x^2 + 7x + 1} $

Left bottom box: $ \boldsymbol{-13x^3 - 4x^2 + 7x + 1} $

Right bottom box: $ \boldsymbol{-4x^3 + x^2 + 6x} $

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Question

Explanation:

Step1: Let the unknown polynomial be \( A \). So the equation is \( -9x^3 - 5x^2 + x + 1 = A - (-4x^3 + x^2 + 6x) \).

Step2: To find \( A \), we can rewrite the equation as \( A = -9x^3 - 5x^2 + x + 1 + (-4x^3 + x^2 + 6x) \).

Step3: Combine like terms. For the \( x^3 \) terms: \( -9x^3 + (-4x^3) = -13x^3 \). For the \( x^2 \) terms: \( -5x^2 + x^2 = -4x^2 \). For the \( x \) terms: \( x + 6x = 7x \). The constant term is \( 1 \). So \( A = -13x^3 - 4x^2 + 7x + 1 \).

Answer: