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factoring trinomials: ax 2 + bx + c

factoring trinomials: ax 2 + bx + c. pp 138-139, text. OBJECTIVE:. find the factors of a trinomial of the form ax 2 + bx + c. factoring trinomials: ax 2 + bx + c. Review of past lessons. factors:. numbers or variables that make up a given product. GCF:.

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factoring trinomials: ax 2 + bx + c

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  1. factoring trinomials:ax2 + bx + c pp 138-139, text OBJECTIVE: • find the factors of a trinomial of the form ax2 + bx + c

  2. factoring trinomials:ax2 + bx + c Review of past lessons • factors: numbers or variables that make up a given product • GCF: greatest number that could be found in every set of factors of a given group numbers • binomial: a polynomial of two terms • trinomial: a polynomial of three terms

  3. factoring trinomials:ax2 + bx + c Review of past lessons • coefficient: the numerical factor next to a variable • exponent: the small number on the upper hand of a factor that tells how many times it will used as factor • binomial: a polynomial of two terms • trinomial: a polynomial of three terms

  4. factoring trinomials:ax2 + bx + c Review of past lessons ( x + 4)2 = x2 + 4x + 16 ( b - 3)2 = b2 - 6b + 9 ( y - 5) ( y + 3) = y2 - 2y -15 ( m - 7) ( m + 7) = m2 - 49 = (a + 8)2 ( a2+16a+64) = ( )( ) a a + 8 + 8 ( ) ( 4a2+20a+24) = 4 a2 +5a + 6

  5. factoring trinomials:ax2 + bx + c ( ) (4a2+20a+24) = 4 a2 +5a + 6 = 4 (a2 + 5a + 6) a ( ) + 3 a ( ) + 2 = 4

  6. Example 1. Factor 12y2 – y – 6 12y2 – y – 6 Find the product of the coefficient of the first term (12) and the last term (–6). 12(-6) = -72 Find the factors of -72 that will add up to -1. -72 = -9, 8 -9 + 8 = -1 Use the factors -9 and 8 for the coefficient of the middle term (-1) 12y2 + (– 9+ 8)y – 6 Use the DPMoA 12y2 + (– 9y + 8y) – 6 Remove the parenthesis.

  7. Group terms that have common monomial factors 12y2 – 9y + 8y – 6 (12y2 – 9y) + (8y – 6) Factor each binomial using GCF. 3y (4y– 3) +2 (4y – 3) Use the Distributive Property. ( ) The factored form of 12y2 – y – 6 (4y– 3y) 3y + 2

  8. 3x2 + 4x + 1 Example 2. Factor 3x2 + 4x + 1 Find the product of the coefficient of the first term (3) and the last term (1). 3(1) = 3 Find the factors of 3 that will add up to 4. 3 = 3,1 3 + 1 = 4 Use the factors 3 and 1 for the coefficient of the middle term (4) 3x2 + (3+1)x + 1 Use the DPMoA 3x2 + (3x+ x) + 1 Remove the parenthesis.

  9. Group terms that have common monomial factors 3x2 + 3x + x + 1 (3x2 + 3x) + (x + 1) Factor each binomial using GCF. +(x+1) Use the Distributive Property. 3x (x+ 1) (x + 1) ( ) 3x + 1 The factored form of 3x2 + 4x + 1.

  10. 21y2 – 35y – 56. Example 3. Factor completely 21y2 – 35y – 56 Factor out the GCF. 7(3y2 – 5y – 8) Factor the new polynomial, if possible. Find the product of 3 and -8. -24 Find the factors of -24 that will add up to -5 which is the middle term. Use the -8 + 3 in place of -5 in the middle term. -24 = - 8, 3 Remove the parenthesis. 7[3y2 + (– 8+ 3)y– 8] Group terms that have common monomial factors 7[3y2 – 8y + 3y – 8]

  11. Group terms that have common monomial factors 7[3y2– 8y + 3y – 8] 7[(3y2 – 8y) + (3y – 8)] Take out the GCF from the first binomial. 7[y(3y– 8) + (3y – 8)] Use the Distributive Property. ( ) y + 1 7 (3y– 8) The factored form of 12y2 – y – 6.

  12. factoring trinomials:ax2 + bx + c pp 138-139, text Classwork p 163, Practice book homework p 164, Practice book

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