1. 6.4 and 6.5 Factoring Trinomials
“Using Bottom’s Up Method”

2. Factoring Trinomials Factor a trinomial into two binomials
Example: x² +5x +6 = (x +3)(x +2)
Opposite of Foiling
To check answers Foil
Example: (x+3) (x+2) = x² +5x +6

3. The X factor To begin factoring trinomials draw a BIG X
East and West multiplied together = North
East and West added together =South
North
East
West
South

4. The X Factor 35
1.) 2.)
3.) 4.) 7 4 12 6 9 6 7

5. The X Factor: How to put a trinomial in the X
Make sure the polynomial is in descending order:
ax² +bx +c
Multiply a and c to get the North term
Write b in the South
Find what two numbers add to get the south and multiply to get the north. Those two numbers are your east and west

6. The X Factor: With Trinomials
1.) x² + 8x +15
2.) 3x⁴ + 4x² +1

7. Bottom’s Up Draw your X and do the X Factor
Make East and West your binomials. Divide your leading term’s variable’s exponent by 2:
(ax²+bx+c) = (x + west) (x + East)
(ax⁴ +bx²+c) = (x²+ west) (x²+East)
(ax⁶ +bx³ +c) = (x³ + west) (x³+ East)
** If there are 2 variables:
(ax² +bxy+cy²) = (x + west y) (x+ east y)
Divide West and East by the coefficient of the leading term (usually the number in front of x²)
Simplify (reduce fraction)
Bring the bottom number up in front of x
Check answer by foiling

8. See Examples
1.) x² + 8x+ 15 Check:
2.) 2x² + 7x +3 Check:

9. Examples
3.) x² + 7xy + 12y² Check:
4.) 6x⁴ +17x² + 5 Check: