1. Ch. 5.4: Factoring (PART 1)

2. GCF: Pull common term out from all terms
Ex:
Pull out 2x
Pull out 3
Pull out 6xy

3. Difference of squares:
Take the square root of the two terms and plug them into the equation above
To simplify exponents, divide by 2
Ex: Ex:
Ex:

4. Trinomials with a coefficient of 1
Make a T-table to the right of the problem
Left column: Find terms that multiply to create the coefficient on the 3rd term
Right column: Find terms that add to create the coefficient on the 2nd term
Find the multiples (a and b) that make both columns true
Plug them in as (x+a)(x+b)
To check, FOIL your answer

5. Helpful hints x2+ax+b: Both terms are positive
x2+ax – b: Smaller term is negative
x2 – ax – b: Larger term is negative
x2 – ax + b: Both terms are negative

6. Ex: Factor x2+9x+20 Both Terms are Positive Create T-table
Multiply: Add: 9
Plug into (x+a)(x+b)
1•20 = 20
1+20 = 21
(x+4)(x+5)
2•10 = 20
2+10 = 12
4•5 = 20
4+5 = 9
Terms: 4,5

7. Ex: Factor x2 - 12x + 32 Both Terms are negative Create T-table
Plug into (x+a)(x+b)
Multiply: Add: -12
(x-4)(x-8)
-1•-32 = 32
-1-32 = -33
-2•-16 = 32
-2-16 = -18
-4•-8 = 32
-4+-8 = -12
Terms: -4,-8

8. Ex: Factor x2 + 5x - 24 Smaller term is negative Create T-table
Plug into (x+a)(x+b)
Multiply: Add: 5
(x-3)(x+8)
-1•24 = -24
-1+24 =23
-2•12 = -24
-2+12 = 10
-3•8 = -24
-3+8 = 5
Terms: -3,8