Factoring Polynomials

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  1. Greatest Common Factor:
    • The largest number and greatest amount of
    • variables that are factors of each term.
    • In other words, we're looking for a number that divides evenly into all values.
  2. Identify the GCF among the numbers given using the grouping method:

    20, 24 and 100
    Image Upload 1     or Image Upload 2

    Image Upload 3 or Image Upload 4

    Image Upload 5    or Image Upload 6

    • Use the "factor tree" for 100 if needed:
    • Image Upload 7

    Now, look and see all the factors that appear in all three listings:

    Image Upload 8

    So two factors of 2 are common to all 3 listings. Which gives us the answer:

    GCF = 22 = 4

    Another way to solve this would be to write the product of common prime factors, with each factor raised to the lowest exponent to which it appears. In this example, the only common prime factor is 2. And the smallest exponent to which it appear is the second power.

    Image Upload 9
  3. Identify the GCF among the numbers given:

    30, 75, 90
    15
  4. Identify the GCF:

    20x5 - 8x4 + 12x2
    GCF = 4x2


    20x5 =  Image Upload 10

    8x4  =   Image Upload 11

    12x2 =  Image Upload 12

    Image Upload 13
  5. Identify the GCF:

    18a3b2 - 24a4bc
    6a3b

    • 18a3b2 = 2*3*3*a*a*a*b*b 
    • 24a4bc = 2*2*2*3*a*a*a*a*b*c

    Image Upload 14
  6. Identify the GCF within a binomial:

    3x(3y+7) - 4(2y+7)
    GCF = 2y+7

    3x(3y+7) - 4(2y+7)
  7. Identify the GCF:

    Image Upload 15
    GCF = a + b
  8. Factor out the GCF:

    20x5 - 8x4 + 12x2
    Step 1: Find the GCF: 4x

    Step 2: We want to find a product of the GCF            (4x2) and another polynomial that                when multiplied equals the                          original polynomial.

    Step 3: Use an empty set of parentheses as             a placeholder for three terms:

    4x2 (__ - __+__)

    Step 4: 4x2 times what will give me 20x5 ?

    4x2 (5x3 -__ + __)

    Step 5: 4x2 times what will give me -8x4 ?

    4x2 (__ -2x2 + __)

    • Step 6: 4x2 times what will give me 12x2 ?
    • 4x2 (__ -__ + 3)

    Step 7: You can check using multiplication.

    4x2 (5x3 -2x2 +3)   = 20x5-8x4 +12x2
  9. Factor out the GCF:
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268584
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Factoring Polynomials
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Factoring Polynomials
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