Factor Any Quadratic FAST!

Struggling to factor quadratics like $3x^2 + 7x + 2$? What if I told you there's a simple trick to skip the tedious trial-and-error method and factor them in seconds?

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

The Trick

The 'Slide and Divide' method is your secret weapon for $ax^2 + bx + c$ where $a \neq 1$. 1. **Slide:** Multiply $a$ and $c$. Rewrite the quadratic as $x^2 + bx + (ac)$. 2. **Factor (Simple):** Factor this new, simpler quadratic into $(x+p)(x+q)$, where $p+q=b$ and $pq=ac$. 3. **Divide:** Divide both $p$ and $q$ by the *original* $a$. So, $(x+\frac{p}{a})(x+\frac{q}{a})$. 4. **Bottoms Up:** Simplify fractions. If a denominator remains (i.e., it doesn't divide evenly), move it in front of the $x$ in that factor. **Why it works:** This method essentially transforms the harder $ax^2+bx+c$ into $x^2+bx+ac$, which is easier to factor. The subsequent division by $a$ and 'bottoms up' step correctly scales the factors back to match the original expression. It's a clever way to systematically find the factors without guesswork.

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