Algebra Period 3 (Review)

FACTORING CHECKLIST
Look for a GCF of all terms
2. Binomials - look for difference of two squares
both perfect squares - double hug - one positive, one negative - square roots of both terms
2. Trinomials - look for Trinomial Square (factors as a binomial squared)
first and last must be perfect squares - middle must be double the product of the two square roots
SINGLE hug - square roots of both terms - sign is the middle sign
3. Trinomials - last sign positive - double hug with same sign as middle term - factors that multiply to last and add to middle
4. Trinomials - last sign negative - double hug with different signs, putting middle sign in first hug - factors that multiply to last and subtract to middle - middle sign will always be with the bigger factor
5. Trinomial with "a" coefficient - Use T chart - multiply first to last to get new product - then find factors that multiply to that new produce and either add or subtract to the middle term (use trinomial rules above) - replace middle term with these two factors and place appropriate signs so they will add to the original middle term - proceed as if you have factoring by grouping (see 6 below)
6. 4 term polynomial - factor by grouping - pair of the first 2 terms and then the second 2 terms by placing parentheses around them - make sure you always have a plus sign between the 2 pairs (you may need to double check) - factor out the GCF of each pair - if it factors, there should now be a new GCF - factor that out in front parentheses and place what ever is left in the second parentheses

REMEMBER:
FACTORING WILL NEVER CHANGE THE ORIGINAL VALUE OF THE POLYNOMIAL SO YOU SHOULD ALWAYS CHECK BY MULTIPLYING BACK!!!!