How to factor polynomials: Difference between revisions

Revision as of 01:22, 8 October 2009

Revision as of 01:23, 8 October 2009

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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 />

Example: Factor <math>6x^2+7x-3</math>

===='''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>

===='''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 />

===='''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 />

===='''Step 4===='''

Rewrite the middle term of '''bx''' using the factors found in step 3.

Instead of <math>7x</math>, write <math>6x^2-2x+9x-18</math><br />

===='''Step 5===='''

Factor by grouping.

<math>(6x^2-2x)+(9x-3)</math><br />