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Factoring Trinomials of the Type: x 2 + bx + c

Factoring Trinomials of the Type: x 2 + bx + c. Factoring trinomials is the foundation for solving quadratic equations. This is the easy set of trinomials because when it is in descending order the coefficient of the first term is 1.

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Factoring Trinomials of the Type: x 2 + bx + c

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  1. Factoring Trinomials of the Type: x2+ bx + c Factoring trinomials is the foundation for solving quadratic equations. This is the easy set of trinomials because when it is in descending order the coefficient of the first term is 1. These trinomials are known as trinomials with a leading coefficient of 1. For example: x2 + 3x – 18 y2 – 8y – 20 c2 + 7c + 12 x2 – 10x + 16

  2. Check: (x + 3)(x + 5) x2 + 8x + 15 x2 + 8x + 15 Factoring Trinomials of the Type: x2+ bx + c Factor x2 + 8x + 15. Yes If it is not in descending order, rearrange it so it’s in descending order. Is this in descending order? Is the leading coefficient 1? Yes Find the factors of the last term’s coefficient that add up to the middle term’s coefficient. Find the factors of 15 that add up to 8. Factors of 15 Sum of Factors which does not add up to 8 1 and 15 16 3 and 5 so 3 and 5 are the correct factors 8 Factoring a trinomial results in a binomial times a binomial. x2 + 5x + 3x + 15   Start with ( + 3)( + 5) Fill in the grey boxes with square root of the first term of the trinomial   ( x + 3)( x + 5)

  3. Factoring Trinomials of the Type: x2+ bx + c Factor c2 – 9c + 20. Find the factors of 20 that add up to –9. Because the middle term is negative and the factors have to multiply to be a positive, the factors I will need to try must both be negative. Factors of 20 Sum of Factors –1 and –20 –21 –2 and –10 –12 –4 and –5 –9 ( – 5)( – 4) cc

  4. Factors of –48 Sum of Factors 1 and –48 –47 48 and –1 47 2 and –24 –22 24 and –2 22 3 and –16 –13 16 and –3 13 Factors of –24 Sum of Factors 1 and –24 –23 24 and –1 23 2 and –12 –10 12 and –2 10 3 and –8 –5 Factoring Trinomials of the Type: x2+ bx + c a. Factor x2 + 13x – 48. b. Factor n2 – 5n – 24. Because the last term is negative and the factors have to multiply to be a negative, one factor must be positive while the other must be negative. Find the factors of –48 that add up to 13. Find the factors of –24 that add up to –5. (n + 3)(n – 8) (x + 16)(x – 3)

  5. Factoring Trinomials of the Type: x2+ bx + c 1) x2+ bx + c Both factors must be positive When the last term is positive, both factors will have the same sign 2) x2–bx + c Both factors must be negative 3) x2±bx–c One factor is positive and one factor is negative

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