Question

problem 3: start the area model
use the next three slides to factor ( 10 x ^ { 2 } + x - 2 )
start by labeling the area model for rectangles i and iv. next,
multiply the main diagonal and enter the product into the table.
( 10 x ^ { 2 } + x - 2 = )

Explanation:

Step1: Identify the terms for rectangle I and IV

In a quadratic \(ax^{2}+bx + c\) (here \(a = 10\), \(b=1\), \(c=- 2\)), for the area - model method of factoring, rectangle I is \(ax^{2}\) and rectangle IV is \(c\). So, rectangle I has the expression \(10x^{2}\) and rectangle IV has the expression \(-2\).

Step2: Calculate the product of the main diagonal

The product of the main - diagonal (rectangle I and rectangle IV) is \((10x^{2})\times(-2)=-20x^{2}\)

Answer:

Rectangle I: \(10x^{2}\), Rectangle IV: \(-2\), Product of Main Diagonal: \(-20x^{2}\)