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**6.4 and 6.5 Factoring Trinomials**

“Using Bottom’s Up Method”

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**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

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**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

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

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**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

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**The X Factor: With Trinomials**

1.) x² + 8x +15 2.) 3x⁴ + 4x² +1

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**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

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

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

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Perfect Square Trinomials. Form for Perfect Square Trinomials: a 2 + 2ab + b 2 OR a 2 – 2ab + b 2.

Perfect Square Trinomials. Form for Perfect Square Trinomials: a 2 + 2ab + b 2 OR a 2 – 2ab + b 2.

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