Expert Voices Project: Factoring

Step 1: To find the greatest common factor (GCF) of this binomial we

need to list factors for both terms.

Step 2: Now that we listed the factors of both 12 and 24, we choose the

GCF. That means the highest number that can go into both 12 and 24. The

factor that we choose is 12.

Step 3: Now we take the 12 and bring it outside of the binomial

meaning that we divide both terms by 12.

Example) 12m – 24p

Now that we have done, we just need to put it altogether.12m – 24p

1212(m – 2p)

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* This type of question can be factored into a binomial because both terms are perfect squares.

Step 1: First factor out x².Example) x² - 36

Step 2: Find a pair of factors that give you -36 when multiplied and give you 0

when added.

(x )(x )

Step 3: Now that we have a list of all of the factors that give you -36, we

choose the one that gives you 0 when added and -36 when multiplied.

Now all we have to do is put it together:(x )(x )(x – 6)(x + 6)

We can also check if we are correct by actually solving it.(x – 6)(x + 6)

x² + 6x - 6x – 36x² - 36 Back to Table of Contents

Example) x² + 4x + 3 Step 1: First factor out x².

Step 2: Now that we factored out x we need to find out what 2 numbers

multiplied that give you the constant 3 and add to give you the coefficient 4.

Step 3: Now that we have the information we need, we have to put it altogether.

We place the 1 and 3 into the binomial.

(x + )(x + )

Factors of 3:3 and 1

* 3 and 1 multiplied together gives you 3, it also gives you 4 when

added, so this is the pair that we use.

(x + 3)(x + 1)We can check to see if we are correct by solving it.

(x + 3)(x + 1)x² + x + 3x +4

x² +4x + 3

x² + bx + c

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ax² + bx + cStep 1: To factor this type of trinomial we need to find out what a x c is. We

know that a = 2 and c = 12. Multiplied its 24.

Step 2: Now that we know what a x c is, we need to find all the possible factors that add up to b. We know that b = 11.

Example) 2x² + 11x + 12

Step 3: Now that we have our list of factors we choose the pair that adds up to 11 which is 8 and 3.

Step 4: Now rewrite the question and replace the 11x with 8x and 3x, be sure that its 8 first and then 3.

2x² + 11x + 12(2x² + 8x) (3x + 12)

Step 5: Now we take out the common factor in each binomial.(2x² + 8x) (3x + 12)2x(x + 4) 3(x + 4)

Step 6: 2x factors out of the first binomial and 3 factors out of the second binomial. Now we have to make 2x and 3 its own binomial keeping x + 4 as its own binomial as

well.

(2x + 3)(x + 4)

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Factoring ax² + bx + c OR x² + bx + c •http://argyll.epsb.ca/jreed/math9/strand2/factor1.htm• http://www.recitfga.qc.ca/english/activities/sitsat-2006/jean-foster/0-2.htm

Factoring GCF• http://www.algebralab.org/practice/practice.aspx?file=Algebra_Redden4A.xml

Another site that can help is:• www.purplemath.com Check the ‘lessons index’ for all the topics.