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There are three possibilities for factoring a trinomial depending on which type of trinomial it is.
'''Monic Trinomials'''--There is a 1 as the leading coefficient.<br />
<math>x^2+bx+c=(x+d)(x+e),</math>
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<math>x^2-x-6=(x-3)(x+2)</math> because <math>(-3)(2)=-6</math> and <math>-3+2=-1</math><br />
<math>x^2-11x+24=(x-3)(x-8)</math> because <math>(-3)(-8)=24</math> and <math>-3+-8=-11</math>
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'''Non-Monic Polynomials'''--There is a constant other than 1 as the leading coefficient.<br />
<math>ax^2+bx+c=(mx+p)(nx+q)</math><br />
where <math>mn=a</math>, <math>pq=c</math>, and <math>mq+pn=b</math>
==References==
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