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===Non-Monic Trinomials===
A non-monic trinomial has a constant other than 1 as the leading coefficient.<br /><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><br /><br />
Many times students are taught that to factor a non-monic trinomials, they must guess different combinations of m,n,p,and q and then [[FOIL]] the factors to see if they had guessed correctly. There is a method of factoring that, while not often taught, will work.<br /><br />
Example: Factor <math>6x^2+7x-3</math><br /><br />
'''Step 1'''–
Multiply '''a''' and '''c'''. (Multiply the number in front of <math>x^2</math> and the [[constant term|constant]])<br />
Multipy 6 and -3, <math>6(-3)=-18</math><br /><br />
'''Step 2'''
Find factors of '''ac'''.<br />
Find factors of -18: -1(18), 1(-18), -2(9), 2(-9), -3(6), and 3(-6).<br /><br />
'''Step 3'''
Decide which factors of '''ac''' that when added together will give '''b'''.<br />
The combination of -2 and 9 is the one needed since -2+9=7.<br /><br />
'''Step 4'''
Rewrite the middle term of '''bx''' using the factors found in step 3.<br />
Instead of <math>7x</math>, write <math>6x^2-2x+9x-18</math><br /><br />
'''Step 5'''
Factor by grouping.<br />
<math>(6x^2-2x)+(9x-3)</math><br />
<math>2x(3x-1)+3(3x-1)</math>
<math>(3x-1)(2x+3)</math><br /><br />
Therefore <math>6x^2+7x-3=(3x-1)(2x+3)</math>
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