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What is the general procedure for factorizing a trinomial?
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General procedure for factorising a trinomial

• Divide the entire equation by any common factor of the coefficients so as to obtain an equation of the form $a{x}^{2}+bx+c$ where $a$, $b$ and $c$ have no common factors and $a$ is positive.
• Write down two brackets with an $x$ in each bracket and space for the remaining terms:

$\begin{equation*} (\ x\phantom{\rule{2.em}{0ex}})(\ x\phantom{\rule{2.em}{0ex}}) \end{equation*}$

• Write down a set of factors for $a$ and $c$.
• Write down a set of options for the possible factors for the quadratic using the factors of $a$ and $c$.
• Expand all options to see which one gives you the correct middle term $bx$.

$\textbf{Note:}$ If $c$ is positive, then the factors of $c$ must be either both positive or both negative. If $c$ is negative, it means only one of the factors of $c$ is negative, the other one being positive.
Once you get an answer, always multiply out your brackets again just to make sure it really works.

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