Question

fill in the parts - whole model for the following equation.
$(-3x^{2}-4)+(\underline{quadquad}) = 2x^{2}+4x - 13$
\boxed{\

$$\begin{array}{|c|c|}\\hline 2x^{2}+4x - 13\\\\\\hline - 3x^{2}-4&\\boxed{\\quadquad}\\\\\\hline\\end{array}$$

}

Explanation:

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

We have the equation \((-3x^{2}-4)+A = 2x^{2}+4x - 13\), so we need to solve for \( A \) by subtracting \((-3x^{2}-4)\) from both sides.

Step2: Subtract \((-3x^{2}-4)\) from \( 2x^{2}+4x - 13 \)

Using the rule of subtracting polynomials (subtracting a polynomial is adding its opposite), we get:
\( A=(2x^{2}+4x - 13)-(-3x^{2}-4) \)
\( = 2x^{2}+4x - 13 + 3x^{2}+4 \)

Step3: Combine like terms

For the \( x^{2} \) terms: \( 2x^{2}+3x^{2}=5x^{2} \)
For the constant terms: \( - 13 + 4=-9 \)
The \( x \) term remains \( 4x \)
So \( A = 5x^{2}+4x - 9 \)

Answer:

\( 5x^{2}+4x - 9 \)