Factorization by Middle Term Breaking

Factorization by Middle Term Breaking

Example 1

$$\textup{Factorize } x^2+11x+28$$

Solution

\begin{align*} & x^2+11x+28\\ =\,\,& x^2+4x+7x+28\\ =\,\,& x(x+4)+7(x+4)\\ =\,\,& (x+4)(x+7)\\ \end{align*}

Example 2

$$\textup{Factorize } x^2+15x+36$$

Solution

\begin{align*} & x^2+15x+36\\ =\,\,& x^2+3x+12x+36\\ =\,\,& x(x+3)+12(x+3)\\ =\,\,& (x+3)(x+12)\\ \end{align*}

Example 3

$$\textup{Factorize } x^2-7x+12$$

Solution

\begin{align*} & x^2-7x+12\\ =\,\,& x^2-3x-4x+12\\ =\,\,& x(x-3)-4(x-3)\\ =\,\,& (x-3)(x-4)\\ \end{align*}