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*}