➕ Algebra 1 · Factoring
Factoring Out the Greatest Common Factor cheat sheet
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Find the GCF
- Numbers: the largest number that divides every coefficient
- Each letter: only if it is in EVERY term, at its LOWEST exponent
- Multiply the pieces together
- A constant term has no letters, so no letter is in the GCF
Factor it out
- Divide each term by the GCF
- Write GCF(quotients), keeping signs
- A term equal to the GCF leaves a 1
- Check by distributing
Special cases
- Negative leading coefficient: factor out the negative of the GCF
- GCF is 1: nothing to pull out
- a(b + c) + d(b + c) = (b + c)(a + d)
- Completely factored: no common factor greater than 1 left inside
Example
- 6x3 − 9x2 + 12x
- GCF is 3x
- = 3x(2x2 − 3x + 4)
Watch out
- Lowest exponent, not highest
- Do not drop the 1
- Distributing checks correctness, not completeness
Formulas
- Factoring (distributive property backward): ab + ac = a(b + c)
- Factoring out a negative: −ab + ac = −a(b − c)
- Lowest power: xm and xn with m ≤ n have GCF xm, because xn = xm · xn−m
- Common binomial factor: a(b + c) + d(b + c) = (b + c)(a + d)
Factoring Out the Greatest Common Factor cheat sheet from HighSchoolQ.com, for personal study use.