6.4 and 6.5 Factoring Trinomials
“Using Bottom’s Up Method”
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
The X factor
• To begin factoring
trinomials draw a BIG X
North
East
West
South
• East and West multiplied
together = North
• East and West added
together =South
The X Factor
1.)
3.)
7
4
2.)
12
4.)
9
6
35
6
7
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
The X Factor: With Trinomials
1.) x² + 8x +15
2.) 3x⁴ + 4x² +1
Bottom’s Up
1. Draw your X and do the X Factor
2. 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)
4. Divide West and East by the coefficient of the leading term
(usually the number in front of x²)
5. Simplify (reduce fraction)
6. Bring the bottom number up in front of x
7. Check answer by foiling
See Examples
1.) x² + 8x+ 15
2.) 2x² + 7x +3
Check:
Check:
Examples
3.) x² + 7xy + 12y²
4.) 6x⁴ +17x² + 5
Check:
Check: