<p><a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-factoring-quadratic-equations-ii"><span style="font-size:22px">Factoring Quadratic Equations II Exercise</span></a></p><p>Sometimes factoring quadratic equations can be a pain in the ass. In this mountain entry, <span style="color:#27ae60;">Factoring Quadratic Equations II</span>, we'll give you some tips for some of those more annoying quadratic equations.</p>
<p><strong><span style="color:#8e44ad;">What makes factoring a quadratic equation annoying?</span></strong></p>
<p>When the quadratic equation has a coefficient greater than $1$ on the $x^2$ term. For example...</p>
<p>$$y = 3x^2 + 15x + 12$$</p>
<p>What would be the best way to factor this badboy? According to Khan Academy, the best way is to find two integers whose product is $36$ ($3 \times 12$) and whose sum is $15$ (the middle term's coefficient).</p>
<p>We can just start playing with numbers to find that and we'll see that $3$ and $12$ work. </p>
<p>We then write the quadratic as...</p>
<p>$$y = 3x^2 + 3x + 12x + 12$$</p>
<p>We can now group like terms and do a bit of factoring to get our final factored form.</p>
<p>$$y=(3x^2 + 3x) + (12x+12)$$</p>
<p>$$y=3x(x+1) + 12(x+1)$$</p>
<p>$$y=(3x+12)(x+1)$$</p>
<p>Here's another example:</p>
<p>$$y = 2x^2 + 3x - 20$$</p>
<p>We need to find two integers whose product is $-40$ ($2 \times -20$) and whose sum is $3$. After some trial and error, we can see they are $8$ and $-5$.</p>
<p>Now we do the grouping and factoring process:</p>
<p>$$y=2x^2 + 8x - 5x - 20$$</p>
<p>$$y = (2x^2+8x) - (5x+20)$$</p>
<p>$$y=2x(x+4) - 5(x+4)$$</p>
<p>$$y=(2x-5)(x+4)$$</p>