Question

now identify factor pairs of 35x² that add to 12x.
use the factor pairs for the areas of rectangles ii and iii to continue labeling the area model.
$x^{2}+12x + 35=$

Explanation:

Step1: Factor the quadratic expression

For a quadratic expression \(x^{2}+bx + c\), we need to find two numbers \(m\) and \(n\) such that \(m + n=b\) and \(m\times n = c\).
Here, \(b = 12\) and \(c=35\).
We find that \(m = 5\) and \(n=7\) since \(5 + 7=12\) and \(5\times7 = 35\).
The quadratic \(x^{2}+12x + 35\) can be factored as \((x + 5)(x+7)\) using the formula \(x^{2}+(m + n)x+mn=(x + m)(x + n)\).

Answer:

\((x + 5)(x + 7)\)