➕ Algebra 1 · Factoring
Factoring by Grouping cheat sheet
Everything you need on one page. Print it, or switch on test-yourself mode to blur the answers and check your memory.
When to use it
- Four terms, no GCF for all four (take any GCF out first)
- Works with several variables too: xy + 3x + 4y + 12
- Works when the two pairs leave the same binomial
Steps (Great Pairs Match Exactly)
- G: GCF of all four terms first
- P: Pair the terms and take out each pair’s GCF
- M: leftover binomials must Match
- E: Extract the common binomial, then Expand to check
Signs
- Choose each GCF’s sign so the binomials match
- −3x + 12 = −3(x − 4)
- −x + 4 = −(x − 4)
- Do not drop a 1 or −1
When it fails
- Check signs, then rearrange the terms
- No match after that: grouping does not work
- Failing to group does not prove a polynomial is prime
- x3 + 2x2 + 3x + 5: no arrangement matches
Trinomial link
- ax2 + bx + c: find m and n with m × n = a × c, m + n = b
- Split bx into mx + nx, then group
- 2x2 + 7x + 6 = 2x2 + 3x + 4x + 6 = (2x + 3)(x + 2)
Example
- x3 + 3x2 + 2x + 6
- = x2(x + 3) + 2(x + 3)
- = (x + 3)(x2 + 2)
Formulas
- Grouping pattern: ax + ay + bx + by = a(x + y) + b(x + y) = (a + b)(x + y)
- Taking out a negative: −px + pq = −p(x − q)
- Splitting the middle term: ax2 + bx + c = ax2 + mx + nx + c, where m + n = b and m × n = a × c
Factoring by Grouping cheat sheet from HighSchoolQ.com, for personal study use.