Three terms, one shared factor: 6x² + 9x + 12 all divide by 3. These free printable worksheets take the greatest common factor out of a three-term expression.
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With three terms the common factor still comes out in front, but now every term has to be checked, and the one that gets forgotten is the last one. In 6x² + 9x + 12 a child divides the 6 and the 9, reaches the 12, and either drops it or divides it wrong — so the walks divide all three, out loud, one at a time.
GREATEST is still the whole difficulty. All three of 6, 9 and 12 share 3, and that is the biggest number that divides every one — 6 divides the first and last but not the 9, so it is not available. Listing the divisors of each coefficient and taking the largest they all share is what turns this from a guess into a method.
One question from this sheet, worked through a step at a time.
102x² + 187x + 51