➕ Algebra 1 · Factoring
Factoring Trinomials 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 the leading coefficient is 1
- Find integers p, q with pq = c and p + q = b
- Then (x + p)(x + q)
- Check by expanding
Signs
- c > 0: p and q have the same sign, the sign of b (if b = 0, it is prime)
- c < 0: opposite signs, and the larger one in size has the sign of b (if b = 0, they are opposites, like 7 and −7)
When the leading coefficient is not 1: SPLICE
- Strip the GCF, then Product ac
- Look for a pair with product ac and sum b
- Insert: split the middle term
- Common factors of each pair, then pull out the binomial
- Expand to check
Always
- GCF first, and keep it in the answer
- Negative leading coefficient: factor out −1 or a negative GCF
- Completely factored: no factor can be factored further
Special cases
- No integer pair works: prime
- u2 ± 2uv + v2 = (u ± v)2
- x2 − 49 = (x − 7)(x + 7), but x2 + 49 is prime
Formulas
- Multiplying two binomials: (x + p)(x + q) = x2 + (p + q)x + pq
- Factoring $x^2 + bx + c$: x2 + bx + c = (x + p)(x + q) when pq = c and p + q = b
- ac method: Find integers m and n with mn = ac and m + n = b. Then ax2 + bx + c = ax2 + mx + nx + c, and you factor by grouping.
- Perfect square trinomials: u2 + 2uv + v2 = (u + v)2 and u2 − 2uv + v2 = (u − v)2
Factoring Trinomials cheat sheet from HighSchoolQ.com, for personal study use.