Question

question
fill in the parts-whole model for the following equation.
(____) + (-5x³ - 8x² + 7x) = x³ - 6x² + 2x + 1
image of parts-whole model with a top rectangle and two bottom rectangles

Explanation:

Step1: Let the unknown polynomial be \( A \)

Let \( A+(-5x^{3}-8x^{2}+7x)=x^{3}-6x^{2}+2x + 1\). Then \( A=(x^{3}-6x^{2}+2x + 1)-(-5x^{3}-8x^{2}+7x)\)

Step2: Remove the parentheses

\(A=x^{3}-6x^{2}+2x + 1 + 5x^{3}+8x^{2}-7x\)

Step3: Combine like - terms

For the \(x^{3}\) terms: \(x^{3}+5x^{3}=6x^{3}\)
For the \(x^{2}\) terms: \(-6x^{2}+8x^{2}=2x^{2}\)
For the \(x\) terms: \(2x-7x=-5x\)
The constant term is \(1\). So \(A = 6x^{3}+2x^{2}-5x + 1\)

Answer:

\(6x^{3}+2x^{2}-5x + 1\)