  Factoring by Grouping

With factoring by grouping, we always want to put parentheses around the first two terms, and then the last two terms. But notice there is a plus here. That's important. So, remember to put parentheses before the plus and after the plus sign. Next, what we're going to do is factor each one of these individual groupings. The greatest common factor of 16x cubed minus 28x squared is going to be a 4x squared. All that we are going to do is put inside the parentheses what's left over.      It looks like we have a 4 and an x. So, these two would give you the 16x cubed. From this negative 28x squared, we have a minus 7. And to check ourselves, we have this 4x squared times negative 7 equals a negative 28x squared. Now, we bring down our plus sign. We do the same thing to this set of parentheses. So we are going to go ahead and take out the greatest common factor here which is 3. Of course, what we are going to write down is the left overs in the parentheses. We've got 3 times 4x will give us 12x. 3 times negative 7 will give us negative 21. So now notice, we now have one term here and we also have another term here. Now what we can do is take the greatest common factor out of each term, but notice that this time it is a little bit more of a complicated expression. Notice that they have the 4x minus 7 in common. So that's what we are going to factor out. And, of course, we are going to put our set of parentheses beside that. What we have left is this 4x squared and the plus 3.

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