Question

Fill in the parts-whole model for the following equation.
left parenthesis, 2, x, squared, plus, 5, x, minus, 1, right parenthesis, plus, left parenthesis, minus, 8, x, squared, minus, 6, x, minus, 7, right parenthesis, equals, left parenthesis, start underline, end underline, right parenthesis
(2x
2
+5x−1)+(−8x
2
−6x−7)=(
​
)

Answer 1

To fill in the parts-whole model for the equation \((2x^2 + 5x - 1) + (-8x^2 - 6x - 7)\), we first need to combine the two polynomials on the left side.

Let's add the like terms:

1. **Combine the \(x^2\) terms**:
\[
2x^2 + (-8x^2) = 2x^2 - 8x^2 = -6x^2
\]

2. **Combine the \(x\) terms**:
\[
5x + (-6x) = 5x - 6x = -1x \text{ or } -x
\]

3. **Combine the constant terms**:
\[
-1 + (-7) = -1 - 7 = -8
\]

Now we can put all these results together. The result of combining the polynomials is:
\[
-6x^2 - x - 8
\]

So, the equation can be rewritten as:
\[
(2x^2 + 5x - 1) + (-8x^2 - 6x - 7) = (-6x^2 - x - 8)
\]

Now we can fill in the parts-whole model:

\[
\underline{-6x^2 - x - 8}
\]

### Final Answer:
\[
(2x^2 + 5x - 1) + (-8x^2 - 6x - 7) = (-6x^2 - x - 8)
\]