<p><a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-factoring-quadratic-equations-i">Factoring Quadratic Equations I Exercise</a></p><p>When you encounter a quadratic equation, first test if it can be <span style="color:#27ae60;">Factored</span>. That means splitting a quadratic equation into two parts, as seen below:</p>
<p>$$ax^2+bx+c=(x+d)(x+e)$$</p>
<p style="text-align: center;">where $d$ and $e$ are integers.</p>
<p><strong><span style="color:#e74c3c;">My Recommended Process</span></strong></p>
<p>Imagine we have the quadratic equation below:</p>
<p>$$x^2+9x+20=0$$</p>
<ul>
<li><strong>Step 1</strong>: List out the number of ways two integers multiply to the $c$ value (in this case $20$).
<ul>
<li>$1 \times 20$</li>
<li>$2 \times 10$</li>
<li>$4 \times 5$</li>
<li>$-1 \times -20$</li>
<li>$-2 \times -10$</li>
<li>$-4 \times -5$</li>
</ul>
</li>
<li><strong>Step 2</strong>: Figure out which pair of integers sums to the $b$ value (in this case $9$).
<ul>
<li>$4+5=9$</li>
</ul>
</li>
<li><strong>Step 3</strong>: Rewrite in factored form:
<ul>
<li>$(x+4)(x+5)=0$</li>
</ul>
</li>
</ul>
<p>From this factored form, we can easily see that the two solutions for $x$ are $-4$ and $-5$.</p>
<p><strong>NOTE: </strong>The answers are NOT $4$ and $5$ because if you plug those values for $x$ in the equation, it will not equal $0$. </p>