Factoring (Distributive Property in Reverse) Examples Page 3

What is the greatest common factor in the expression 6xy³ - 9x²y³ + 15y²z?

Gee whiz. That's visually a bit daunting, but we are doing the exact same thing; we need to take it piece by piece. The number part will be the largest constant that divides 6, 9, and 15, which is 3. The variable x occurs once in the first term, twice in the second, and not at all in the third, and we don't get to use any copies of x. The variable y occurs three times in the first term, three times in the second term, and twice in the third term, and we get two copies of y. The variable z does not occur in the first two terms, and we don't get any copies of z. We can conclude that the greatest common factor for this expression is 3y². It is a shame, really...z hardly ever gets any time in the spotlight, and here he is getting dissed again. Chin up, z. Your time will come.