FACTORING

1. FACTORING

2. Steps for Factoring Trinomials-Grouping • Power’s are in descending order (x2,x, #) and it is = 0 or = y • Pull out your GCF (Greatest Common Factor), if possible. • Multiply the a-value times the c-value • Finding your “SPECIAL NUMBERS”--Find two numbers that multiply to your number from above (A*C)(step 3) and add to your b-value. • Substitute the numbers that you just got in place of your b-value (since they are equal) • Group your first two terms and group your last two terms. • Pull out the GCF for each group. (If done correctly then what remains in both will be the same) If there is a negative in the front of the parenthesis you must pull out a negative. • Put your two GCF’s together in parenthesis, and bring down one of the groups that were the same. If you pulled out a GCF at the very beginning then put it in the front of everything. • Set each part = 0, and then solve. These will be your solutions

3. Steps for Factoring Trinomials-CAB • Power’s are in descending order (x2,x, #) and it is = 0 or = y • Pull out your GCF (Greatest Common Factor), if possible. • Multiply the a-value times the c-value • Finding your “SPECIAL NUMBERS”--Find two numbers that multiply to your number from above (A*C)(step 3) and add to your b-value. • Take the “SPECIAL NUMBERS” and divide by a-term to get your term. • If it turns out to be a fraction-move the denominator to the front with the x, so it will be the coefficient with the x. • If you pulled out a GCF at the very beginning then put it in the front of everything. • Set each part = 0, and then solve. These will be your solutions

4. Steps for Factoring Trinomials-Box • Power’s are in descending order (x2,x, #) and it is = 0 or = y • Pull out your GCF (Greatest Common Factor), if possible. • Multiply the a-value times the c-value • Finding your “SPECIAL NUMBERS”--Find two numbers that multiply to your number from above (A*C)(step 3) and add to your b-value. • Create the box • Put the entire a-term in upper left corner, and entire c-term in lower left corner. • Put the “Special Numbers with their variables in the other two spaces. • Pull out The GCF from the first row • Pull out the GCF from the second row • Pull out the GCF from the first column • Pull out the GCF from the second column • Put what you pulled out from your rows together, and what you pulled out from your columns together. 11. If you pulled out a GCF at the very beginning then put it in the front of everything. 12. Set each part = 0, and then solve. These will be your solutions

5. Steps for Factoring Trinomials-Trial and Error • Power’s are in descending order (x2,x, #) and it is = 0 or = y • Pull out your GCF (Greatest Common Factor), if possible. • Find all the factors of the a-term, find all the factors of the c term. • Trial and Error • If the C-term is negative then you know one sign will be positive and one negative. If the b-term is negative then the larger term will be negative. If the b-term is positive then the larger term will be positive. • If the C-term is positive then your signs will either be either both positive or both negative, it will be determined by your b-term. • It sometimes is easiest to start with the term that has the least amount of factors. • If you pulled out a GCF at the very beginning then put it in the front of everything. • Set each part = 0, and then solve. These will be your solutions