Does every term share a factor? On a two-term expression like 12x + 18 that is the first thing to try. These free printable worksheets take out the greatest common factor.
Taking out a common factor is the step students skip on the way to everything else, and on two terms it is at its clearest. Look at 12x + 18: both numbers are even, both divide by 3, so 6 comes out in front and 6(2x + 3) is left. Do it first and every later step is smaller; skip it and the numbers stay big.
Why this sheet works
The word carrying the difficulty is GREATEST. 12x + 18 shares 2, and 3, and 6 — only 6 finishes the job. A child who stops at 2 writes 2(6x + 9), which still has a 3 hiding inside. So the walks list what divides each coefficient and take the biggest they all share, rather than announcing a number.
How this one works
One question from this sheet, worked through a step at a time.
120x + 168
120x + 168
120168
120:12345681012152024304060120
168:12346781214212428425684168
24 × (5x + 7)
120x + 168=24(5x + 7)
Before anything else, look at whether every term shares a factor. The numbers here are 120, 168 — so the question is what the biggest number that divides ALL of them is.
List what divides each one and look for the biggest they all share. 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 168: 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168.
The biggest number in all of those lists is 24. Take it out in front and divide every term by it: 120 ÷ 24 = 5, 168 ÷ 24 = 7.
Check the bracket before you stop. 5x + 7 — those numbers share nothing but 1, so there is no more to take out and 24 really was the greatest. 120x + 168 = 24(5x + 7).
