Question

fill in the parts - whole model for the following equation.
$7x^{2}+5x - 7 = (\\_\\_\\_) - (-5x^{2}+3x + 10)$

Explanation:

Step1: Let the unknown polynomial be \( A \). So the equation is \( 7x^{2}+5x - 7=A-(- 5x^{2}+3x + 10) \)

Step2: Solve for \( A \) by adding \( -5x^{2}+3x + 10 \) to both sides. \( A=(7x^{2}+5x - 7)+(-5x^{2}+3x + 10) \)

Step3: Combine like terms. \( 7x^{2}-5x^{2}=2x^{2} \), \( 5x + 3x = 8x \), \( -7 + 10 = 3 \)

Step4: So \( A = 2x^{2}+8x + 3 \)

Answer:

The unknown polynomial is \( 2x^{2}+8x + 3 \), and the parts - whole model has the whole as \( 7x^{2}+5x - 7 \) and the two parts as \( 2x^{2}+8x + 3 \) and \( - 5x^{2}+3x + 10 \) (with the first part being the one we found and the second part being the subtrahend in the original equation). The filled - in polynomial for the blank is \( 2x^{2}+8x + 3 \)