6.4 and 6.5 Factoring Trinomials

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 • East and West multiplied together = North • East and West added together =South North East West South

The X Factor 35 1.) 2.) 3.) 4.) 7 4 12 6 9 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 • 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) 5. Simplify (reduce fraction) • Bring the bottom number up in front of x • Check answer by foiling

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

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

6.4 and 6.5 Factoring Trinomials