Factoring Made Easy: The 'Reverse FOIL' Trick

Struggling with factoring quadratics? What if you could 'undo' FOIL to find the factors almost instantly?

Subject: algebra • Classes: 6–12 • Difficulty: intermediate (9-10)

The Trick

The 'Reverse FOIL' trick leverages the FOIL (First, Outer, Inner, Last) method in reverse to factor quadratic expressions of the form $ax^2 + bx + c$ (where $a=1$). First, find two numbers that multiply to $c$ and *add* to $b$. Let's call them $p$ and $q$. Then, the factored form is simply $(x+p)(x+q)$. This works because when you FOIL $(x+p)(x+q)$, you get $x^2 + px + qx + pq = x^2 + (p+q)x + pq$. Therefore, $p+q$ must equal $b$, and $pq$ must equal $c$.

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