SOLUTION: Hi I need to know the steps on how to calculate the GCF of a polynomial please?

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Question 203222: Hi I need to know the steps on how to calculate the GCF of a polynomial please?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
  1. Factor each term (mentally or on paper)
    • Factor the coefficient into prime factors
    • Rewrite any variables with exponents without exponents. For example, x%5E6 becomes x%2Ax%2Ax%2Ax%2Ax%2Ax
  2. Now you have a list of factors for each term. Compare these lists looking for the longest string of factors which is in every list of factors. Remember, order of factors is not significant! This longest list of common factors is the GCF.
  3. Rewrite the polynomial in factored form:
    1. Write the GCF
    2. Write a left parenthesis
    3. Write each term from its list of factors. Omit the factors of the GCFand separate the terms with "+" and "-" as they were in the original polynomial.
    4. Write a right parenthesis
    4. Recombine the factors. (Do not use the distributive property!)
    1. Multiply together the individual factors of the GCF.
    2. Multiply together the individual factors of the terms in the parentheses.

Here's an example:
12x%5E7+%2B+30x%5E5+-+42x%5E3+%2B+60x%5E2
1. Factor each term
12x%5E7+=+2%2A2%2A3%2Ax%2Ax%2Ax%2Ax%2Ax%2Ax%2Ax
30x%5E5+=+2%2A3%2A5%2Ax%2Ax%2Ax%2Ax%2Ax
42x%5E3+=+2%2A3%2A7%2Ax%2Ax%2Ax
60x%5E2+=+2%2A2%2A3%2A5%2Ax%2Ax

2. Compare these lists looking for the longest string of factors found in every term. Until you develop a better eye for this you might want to line up the factors like below. Note how the spacing of factors is adjusted as needed to line up the common factors:
2*2*3*    x*x*x*x*x*x*x
2*  3*5*  x*x*x*x*x
2*  3*  7*x*x*x
2*2*3*5*  x*x

From this point of view we should be able to see the following factors are in all four terms: 2, 3, x and a second x. So the GCF is 2*3*x*x

3. Write the GCF, a left parenthesis, the "remainders" of the other terms and a right parenthsis. Please make sure you understand where all of the following comes from:
2%2A3%2Ax%2Ax%282%2Ax%2Ax%2Ax%2Ax%2Ax+%2B+5%2Ax%2Ax%2Ax+-+7%2Ax+%2B+2%2A5%29

4. Recombine the factors
6x%5E2%282x%5E5+%2B+5x%5E3+-+7x+%2B+10%29