Sample Problemįactor the expression -50 x + 4 y in two different ways. We'll show you what we mean grab a bunch of negative signs and follow us. Sometimes we have a choice of factorizations, depending on where we put the negative signs. This step will get us to the greatest common factor. Finally, multiply together the number part and each variable part. Use that number of copies (powers) of the variable. Both to do and to explain.įor each variable, find the term with the fewest copies. The variable part of a greatest common factor can be figured out one variable at a time. The number part of the greatest common factor will be the largest number that divides the number parts of all the terms. To find the greatest common factor for an expression, look carefully at all of its terms. Not that that makes 9 superior or better than 3 in any way it's just that.well, 3 is simply.oy. The terms in parentheses have nothing else in common to factor out, and 9 was the greatest common factor. Instead, let's be greedy and pull out a 9 from the original expression. This is us desperately trying to save face. As great as you can be without being the greatest. Although it's still great, in its own way. We can factor this expression even further because all of the terms in parentheses still have a common factor, and 3 isn't the greatest common factor. Right off the bat, we can tell that 3 is a common factor. Let's find ourselves a GCF and call this one a night. That would be great, because as much as we love factoring and would like nothing more than to keep on factoring from now until the dawn of the new year, it's almost our bedtime. The greatest common factor is a factor that leaves us with no more factoring left to do it's the finishing move. When we factor an expression, we want to pull out the greatest common factor. If these two ever find themselves at an uncomfortable office function, at least they'll have something to talk about. The value 3 x in the example above is called a common factor, since it's a factor that both terms have in common. We do, and all of the Whos down in Whoville rejoice. We can check that our answer is correct by using the distributive property to multiply out 3 x( x – 9 y), making sure we get the original expression 3 x 2 – 27 xy. Since each term of the expression has a 3 x in it (okay, true, the number 27 doesn't have a 3 in it, but the value 27 does), we can factor out 3 x: Sample Problemįactor the expression 3 x 2 – 27 xy. Factoring expressions is pretty similar to factoring numbers.
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