Factor out the GCF Practice

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In this section, we review how to factor out the GCF (Greatest Common Factor). Recall that the GCF is the largest common factor of a group of numbers. The GCF is also known as the GCD or greatest common divisor. We can think of a factor as a divisor, and we can say that the GCF or GCD is the largest number that a group of numbers is divisible by. To find the GCF/GCD for a group of terms, we split the operation into finding the number part and the variable part. For the number part, we find the prime factorization of each number. We then multiply together all prime factors that are common to each number of the group. For the variable part, we use a similar process. We simply need to make sure the variable is common to each term in the group. We can then look at the smallest exponent that appears on that variable. This will give us what is common to all members of the group. Placing the number part and the variable part together give us the GCF. Once we have reviewed how to find the GCF, we then move into factoring. We can factor out the GCF from a polynomial by placing the polynomial inside of parentheses. We then place the GCF outside of that set of parentheses. Lastly, we divide each term of the polynomial inside of the parentheses by the GCF to obtain the new terms inside of the parentheses. We can always check the result with the distributive property.
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