Factoring Methods
For every factoring problem:
1 Factor out the GCF, if possible. Always!!
2 Count the number of terms
- If 4 terms (or more): Factor by grouping
- If 3 terms (or more):
● If of the form, 𝑎𝑥 2 + 𝑏𝑥 + 𝑐, where 𝑎 ≠ 1
● Find 2 numbers, such that m and n such that
𝑚●𝑛 = 𝑎𝑐, and 𝑚 + 𝑛 = 𝑏 and do factor by
grouping.
● If of the form, 𝑥 2 + 𝑏𝑥 + 𝑐, then find two numbers
𝑚 𝑎𝑛𝑑 𝑛 such that: ●𝑛 = 𝑐 𝑎𝑛𝑑 𝑚 + 𝑛 = 𝑏.
Answer will be → 𝑥 2 + 𝑏𝑥 + 𝑐 = (𝑥 + 𝑚)(𝑥 + 𝑛)
- If 2 terms: We match with the formulas, if we can.
● 𝑎2 − 𝑏2 = (𝑎 − 𝑏)(𝑎 + 𝑏)
● 𝑎 2 + 𝑏2 : 𝑝𝑟𝑖𝑚𝑒 𝑐𝑎𝑛′ 𝑡 𝑏𝑒 𝑓𝑎𝑐𝑡𝑜𝑟𝑒𝑑‼‼
● 𝑎 3 − 𝑏3 = (𝑎 − 𝑏)(𝑎 2 + 𝑎𝑏 + 𝑏2 )
● 𝑎3 + 𝑏3 = (𝑎 + 𝑏)(𝑎 2 − 𝑎𝑏 + 𝑏2 )