Question

problem 1: complete the area model
now identify factor pairs of $30x^{2}$ that add to $11x$.
use the factor pairs for the areas of rectangles ii and iii to continue labeling the area model.
$3x^{2}+11x + 10=$

Explanation:

Step1: Factor the quadratic expression

For a quadratic expression \(ax^{2}+bx + c\) (here \(a = 3\), \(b=11\), \(c = 10\)), we need to find two numbers \(m\) and \(n\) such that \(m\times n=ac=3\times10 = 30\) and \(m + n=b = 11\). The numbers are \(5\) and \(6\).
We rewrite the middle - term: \(3x^{2}+11x + 10=3x^{2}+6x+5x + 10\).

Step2: Group the terms

Group the terms as \((3x^{2}+6x)+(5x + 10)\).
Factor out the common factors from each group: \(3x(x + 2)+5(x + 2)\).

Step3: Factor out the common binomial factor

Since \((3x(x + 2)+5(x + 2))=(3x + 5)(x+2)\)

Answer:

\((3x + 5)(x + 2)\)